el muchacho Comfortably Numb | Ca fait des trucs un peu moches, qui "bavent" un peu parfois. Mais c'est quand même super utile pour du prototypage, du design, de l'architecture, etc...
nraynaud a écrit :
j'pense pas. C'est juste l'inversion naïve d'une matrice 4x4, mais numériquement ça tient pas la marrée.
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Ch'uis allé voir le code d'une lib de calcul de raytracing pour les simulations de trous noirs (libMotion4D). Il y a des milliers de lignes de code de ce genre là: Code :
- /*! Calculate the Christoffel symbols of the second kind at position 'pos'.
- *
- * \param pos : pointer to position.
- */
- bool MetricHartleThorneGB::calculateChristoffels( const double* pos ) {
- double M = mMass;
- double a = mAngmom;
- double eta = mEta;
- double r = pos[1];
- double theta = pos[2];
- calcFuncDiff(pos);
- double t1 = sigma; // Sigma(r,theta);
- double t2 = t1*t1;
- double t3 = t2*t2;
- double t4 = 1/t3;
- double t5 = delta; // Delta(r);
- double t6 = t5*t5;
- double t7 = t4*t6;
- double t8 = a*a;
- double t9 = eta*t8;
- double t10 = hrr; // hrr(r,theta);
- double t11 = t1*t10;
- double t14 = 1/(t5+t9*t11);
- double t15 = M*t2;
- double t17 = M*r;
- double t18 = dsigmadr; // diff(Sigma(r,theta),r);
- double t19 = t18*t1;
- double t22 = t2*t1;
- double t23 = dhttdr; // diff(htt(r,theta),r);
- double t24 = t22*t23;
- double t26 = t9*t2;
- double t27 = t23*M;
- double t28 = t27*r;
- double t31 = t9*t1;
- double t32 = htt; // htt(r,theta);
- double t33 = t32*t18;
- double t34 = t33*t17;
- double t37 = t2*t32;
- double t41 = M*M;
- double t42 = t23*t41;
- double t43 = r*r;
- double t44 = t42*t43;
- double t47 = t32*t41;
- double t48 = t47*r;
- double t51 = t8*t8;
- double t52 = eta*t51;
- double t53 = t52*t1;
- double t54 = t41*r;
- double t55 = sin(theta);
- double t56 = t55*t55;
- double t57 = t56*t56;
- double t58 = hphph; // hpp(r,theta);
- double t59 = t57*t58;
- double t60 = t54*t59;
- double t63 = t41*t43;
- double t64 = dhppdr; // diff(hpp(r,theta),r);
- double t65 = t57*t64;
- double t70 = t47*t43;
- double t74 = t63*t59;
- double t77 = 2.0*t15-2.0*t17*t19+t9*t24-4.0*t26*t28+4.0*t31*t34-4.0*t9*t37*M+4.0*t31*t44+8.0*t31*t48+8.0*t53*t60+4.0*t53*t63*t65-8.0*t9*t18*t70-8.0*t52*t18*t74;
- double t81 = hthth; // haa(r,theta);
- double t82 = t1*t81;
- double t85 = 1/(1.0+t9*t82);
- double t86 = t4*t85;
- double t87 = dsigmadth; // diff(Sigma(r,theta),theta);
- double t88 = t87*t1;
- double t89 = t17*t88;
- double t91 = dhttdth; // diff(htt(r,theta),theta);
- double t92 = t22*t91;
- double t94 = t91*M;
- double t95 = t94*r;
- double t98 = t32*t87;
- double t99 = t98*t17;
- double t102 = t91*t41;
- double t103 = t102*t43;
- double t106 = t1*t41;
- double t107 = t52*t106;
- double t108 = t56*t55;
- double t109 = t43*t108;
- double t110 = cos(theta);
- double t111 = t58*t110;
- double t112 = t109*t111;
- double t115 = dhppdth; // diff(hpp(r,theta),theta);
- double t116 = t57*t115;
- double t129 = 1/t2;
- double t130 = t8*t22;
- double t133 = t43*t22;
- double t134 = t133*M;
- double t136 = t56*t58;
- double t137 = t52*t136;
- double t138 = t43*r;
- double t139 = t138*t2;
- double t140 = M*t18;
- double t141 = t139*t140;
- double t144 = eta*eta;
- double t145 = t51*t8;
- double t146 = t144*t145;
- double t147 = t146*t136;
- double t148 = t33*M;
- double t152 = t138*t22;
- double t153 = t152*t27;
- double t158 = 16.0*t147*t139*t47;
- double t159 = t8*t2;
- double t160 = t17*t18;
- double t163 = t146*t56;
- double t164 = t58*t43;
- double t165 = t3*t23;
- double t170 = t8*t32;
- double t172 = t133*eta*t170*M;
- double t174 = t51*t22;
- double t175 = t174*eta;
- double t179 = t51*t51;
- double t180 = t144*t179;
- double t181 = t180*t56;
- double t182 = t58*t22;
- double t183 = t32*M;
- double t187 = t51*t2;
- double t188 = t187*eta;
- double t191 = eta*t32;
- double t195 = eta*t145;
- double t196 = t195*t136;
- double t197 = r*t18;
- double t201 = t58*t3;
- double t204 = t57*t56;
- double t205 = t58*t58;
- double t206 = t204*t205;
- double t207 = t180*t206;
- double t208 = t43*t43;
- double t209 = t208*t1;
- double t210 = t18*t41;
- double t213 = 8.0*t207*t209*t210;
- double t214 = t180*t136;
- double t218 = t146*t59;
- double t219 = t208*t2;
- double t220 = t219*t42;
- double t221 = t218*t220;
- double t223 = t47*t18;
- double t224 = t209*t223;
- double t226 = 8.0*t218*t224;
- double t228 = t51*t3;
- double t229 = eta*t23;
- double t231 = -4.0*t181*t182*t183+8.0*t188*t48-4.0*t174*t191*M-2.0*t196*t15*t197+t181*t201*t23-t213+4.0*t214*t37*t160-12.0*t221+t226-2.0*t141+t228*t229;
- double t233 = t208*r;
- double t234 = t233*t145;
- double t235 = t41*M;
- double t236 = t235*t57;
- double t237 = t234*t236;
- double t238 = t144*t32;
- double t239 = t1*t64;
- double t240 = t238*t239;
- double t242 = 8.0*t237*t240;
- double t245 = t235*t32;
- double t248 = 8.0*t218*t209*t245;
- double t249 = t144*t51;
- double t250 = t249*t136;
- double t251 = t208*t43;
- double t252 = t251*t1;
- double t256 = t152*eta;
- double t257 = t8*t23;
- double t258 = t257*M;
- double t261 = t219*eta;
- double t265 = t139*eta;
- double t268 = 8.0*t265*t170*t41;
- double t273 = t146*t204;
- double t274 = t205*t233;
- double t278 = 4.0*t273*t274*t2*t41;
- double t280 = t233*t2;
- double t282 = t250*t280*t47;
- double t284 = t146*t206;
- double t287 = 4.0*t284*t252*t210;
- double t288 = t204*t58;
- double t289 = t180*t288;
- double t290 = t235*t138;
- double t291 = t290*t33;
- double t293 = 8.0*t289*t291;
- double t294 = t9*t136;
- double t298 = t249*t56;
- double t299 = t58*t208;
- double t302 = t209*eta;
- double t307 = t33*t63;
- double t310 = t233*t22;
- double t314 = t145*t1;
- double t319 = t56*t41;
- double t320 = t319*t51;
- double t321 = t43*t2;
- double t322 = t321*t229;
- double t325 = t56*M;
- double t326 = t325*t51;
- double t327 = r*t22;
- double t331 = 8.0*t282-t287-t293-2.0*t294*t280*t140+t298*t299*t165-8.0*t302*t8*t18*t47-8.0*t53*t307-4.0*t250*t310*t27-8.0*t314*eta*t18*t74-4.0*t320*t322+2.0*t326*t327*t229;
- double t334 = t43*t145;
- double t335 = t334*t319;
- double t336 = t32*t32;
- double t337 = t144*t336;
- double t340 = 4.0*t335*t337*t19;
- double t341 = t52*t56;
- double t342 = t22*M;
- double t343 = t164*t342;
- double t344 = t341*t343;
- double t346 = t138*t179;
- double t347 = t235*t204;
- double t348 = t346*t347;
- double t350 = 8.0*t348*t240;
- double t351 = t208*t145;
- double t352 = t41*t57;
- double t353 = t351*t352;
- double t354 = t2*t64;
- double t355 = t238*t354;
- double t356 = t353*t355;
- double t358 = t195*t56;
- double t359 = t182*M;
- double t362 = t43*t179;
- double t363 = t362*t352;
- double t364 = t363*t355;
- double t366 = t346*t236;
- double t368 = 8.0*t366*t240;
- double t369 = t179*t8;
- double t370 = t144*t369;
- double t371 = t57*t57;
- double t372 = t370*t371;
- double t373 = t205*t235;
- double t374 = t138*t18;
- double t377 = 8.0*t372*t373*t374;
- double t380 = t56*t144;
- double t384 = 4.0*r*t145*t41*t380*t336*t2;
- double t385 = t43*t3;
- double t386 = t9*t23;
- double t389 = t208*t22;
- double t391 = t250*t389*t183;
- double t393 = t251*t2;
- double t397 = t205*t1;
- double t398 = t235*t43;
- double t401 = 8.0*t372*t397*t398;
- double t402 = t180*t59;
- double t403 = t1*t235;
- double t405 = t403*t138*t23;
- double t407 = 8.0*t402*t405;
- double t408 = t19*t70;
- double t411 = t370*t204;
- double t412 = t205*t2;
- double t415 = 4.0*t411*t412*t54;
- double t416 = t37*t54;
- double t421 = t170*t140;
- double t425 = 8.0*t289*t405;
- double t427 = 8.0*t402*t291;
- double t428 = -4.0*t391+4.0*t250*t393*t42+t401+t407-8.0*t214*t408+t415+8.0*t214*t416-16.0*t147*t224+4.0*t265*t421-t425-t427;
- double t431 = 8.0*t402*t408;
- double t433 = t2*t23*t63;
- double t437 = 8.0*t402*t416;
- double t438 = t209*t52;
- double t442 = t1*t32;
- double t443 = t398*t442;
- double t445 = 8.0*t289*t443;
- double t446 = t402*t433;
- double t451 = 8.0*t402*t443;
- double t452 = t370*t206;
- double t455 = 4.0*t452*t19*t63;
- double t456 = t233*t1;
- double t460 = 8.0*t218*t456*t235*t23;
- double t461 = t233*t235;
- double t464 = 8.0*t218*t461*t33;
- double t465 = t431+4.0*t214*t433-t437-8.0*t438*t210*t59+t445-12.0*t446+4.0*t289*t433+t451-t455+t460-t464;
- double t466 = t180*t371;
- double t467 = t205*t208;
- double t470 = 8.0*t466*t467*t403;
- double t474 = 8.0*t466*t274*t235*t18;
- double t475 = t24*t17;
- double t481 = t147*t133*t183;
- double t488 = t145*t2;
- double t489 = t488*eta;
- double t492 = t9*t56;
- double t494 = t492*t299*t342;
- double t496 = t336*t1;
- double t499 = 8.0*t163*t398*t496;
- double t500 = t336*t18;
- double t503 = 8.0*t163*t290*t500;
- double t504 = -t470-t474-4.0*t214*t475+4.0*t402*t475-8.0*t481+4.0*t218*t153+4.0*t250*t280*t148+8.0*t489*t60+2.0*t494+t499-t503;
- double t509 = M*t138;
- double t510 = t509*t1;
- double t514 = t52*t57;
- double t515 = t58*t138;
- double t516 = t1*M;
- double t520 = t146*t32;
- double t521 = t41*t208;
- double t525 = t180*t32;
- double t529 = M*t233;
- double t538 = t249*t32;
- double t546 = t51*t57;
- double t557 = t52*t32;
- double t558 = t1*t56;
- double t562 = t146*t442;
- double t573 = 2.0*t510-t159-4.0*t341*t70-4.0*t514*t515*t516-t321+8.0*t520*t521*t136+4.0*t525*t63*t136+2.0*t529*t1*t294+4.0*t9*t47*t208+4.0*t52*t70+4.0*t538*t41*t251*t136+4.0*t510*t137+4.0*t521*eta*t546*t58+4.0*t63*eta*t145*t57*t58+t9*t37*t43+2.0*t557*t558*t17-8.0*t562*t509*t136-4.0*t249*t442*t529*t136-8.0*t520*t521*t59;
- double t574 = t180*t442;
- double t583 = t9*t32;
- double t586 = t516*r;
- double t589 = t136*t2;
- double t591 = t195*t57;
- double t592 = t58*t1;
- double t596 = t195*t204;
- double t598 = t58*t41*t43;
- double t604 = t59*t17;
- double t609 = t164*t2;
- double t616 = t2*t56;
- double t617 = t616*t164;
- double t625 = t52*t37;
- double t629 = -4.0*t574*t17*t136-8.0*t525*t74+4.0*t525*t288*t63-4.0*t583*t510-4.0*t557*t586-t195*t589-4.0*t591*t592*t17-4.0*t596*t598+4.0*t562*t59*t509+4.0*t574*t604-t492*t299*t2-2.0*t341*t609-2.0*t325*t8*r*t1+2.0*t520*t617+t538*t616*t299+t525*t589+2.0*t586*t196+t625+2.0*t17*t1*t8;
- double t631 = 1/(t573+t629);
- double t633 = t129*(4.0*t261*t257*t41+2.0*t130*M-8.0*t250*t252*t223-t242-4.0*t172-4.0*t175*t28+8.0*t147*t139*t148+2.0*t163*t164*t165-4.0*t256*t258-t248-t278+t331+t158-2.0*t159*t160+2.0*t358*t359-8.0*t147*t153+t350+4.0*t356+t340+4.0*t344+8.0*t147*t220-t384+t385*t386-t368+t428-4.0*t137*t141+t465+t504+t268+4.0*t188*t44+4.0*t188*t34+2.0*t134+4.0*t364-t377+t231)*t631/2.0;
- double t634 = a*M;
- double t635 = t515*t24;
- double t637 = M*t43;
- double t639 = t56*t64;
- double t640 = t52*t639;
- double t643 = t456*t42;
- double t646 = t249*t47;
- double t650 = M*t208;
- double t652 = t9*t639;
- double t658 = t467*t106;
- double t665 = t274*t210;
- double t668 = t180*t204;
- double t670 = t41*t138;
- double t671 = t205*t18*t670;
- double t674 = t515*t15;
- double t677 = t146*t47;
- double t678 = t138*t1;
- double t682 = t136*t22;
- double t684 = t1*t23;
- double t685 = t670*t684;
- double t688 = t298*t635-2.0*t637*t2*t640+4.0*t250*t643-4.0*t646*t456*t639-2.0*t650*t2*t652-4.0*t250*t209*t47-4.0*t273*t658-4.0*t250*t233*t18*t47-4.0*t273*t665-4.0*t668*t671-4.0*t492*t674-4.0*t677*t678*t639+t52*t682-4.0*t218*t685;
- double t689 = t321*t27;
- double t692 = t43*t18;
- double t697 = t146*t37;
- double t698 = r*t56;
- double t699 = t58*t18;
- double t700 = t698*t699;
- double t702 = t43*t57;
- double t703 = t64*M;
- double t704 = t702*t703;
- double t707 = t249*t336;
- double t708 = t1*t43;
- double t709 = t708*t140;
- double t715 = t327*t639;
- double t720 = t146*t183;
- double t721 = t321*t639;
- double t724 = t249*t183;
- double t725 = t138*t56;
- double t726 = t58*t2;
- double t732 = t219*t27;
- double t737 = t33*t670;
- double t740 = -4.0*t147*t689+4.0*t562*t692*t59*M+t697*t700-2.0*t697*t704+4.0*t707*t709-4.0*t677*t374*t59-t520*t715+4.0*t677*t708*t59+4.0*t720*t721+8.0*t724*t725*t726+2.0*t218*t689-4.0*t250*t732-4.0*t697*t604-4.0*t147*t737;
- double t742 = t183*r;
- double t745 = t32*t22;
- double t748 = t219*t639;
- double t751 = t63*t1;
- double t760 = t9*t138;
- double t761 = t22*t56;
- double t762 = t761*t64;
- double t769 = t761*t164;
- double t772 = t52*r;
- double t774 = t152*t639;
- double t776 = t249*t37;
- double t779 = t52*t43;
- double t780 = t2*t57;
- double t784 = 4.0*t26*t742-2.0*t9*t745+4.0*t724*t748+4.0*t707*t751-4.0*t707*t670*t18+4.0*t677*t678*t65+t760*t762+4.0*t188*t604+3.0*t492*t164*t22-3.0*t538*t769+t772*t762-t538*t774+t776*t725*t699+2.0*t779*t780*t703;
- double t785 = t197*t2;
- double t788 = t397*t63;
- double t791 = t15*r;
- double t794 = t616*t699;
- double t796 = t9*r;
- double t802 = t182*r*t23;
- double t806 = t442*t63;
- double t809 = t1*eta;
- double t810 = t51*t43;
- double t813 = t58*M;
- double t814 = t18*t57*t813;
- double t817 = t692*t183;
- double t820 = t336*t22;
- double t822 = -t707*t785-t520*t682+4.0*t668*t788-4.0*t707*t791-t772*t794+2.0*t796*t37*t18-t760*t794+t163*t802+4.0*t147*t685+4.0*t147*t806-4.0*t809*t810*t814-4.0*t31*t817+t22+t249*t820-t785;
- double t827 = t634*t129*(t688+t740+t784+t822)*t631;
- double t828 = t41*t108;
- double t830 = t2*t110;
- double t831 = t830*t58;
- double t832 = t238*t831;
- double t835 = t57*t108;
- double t836 = t835*t205;
- double t837 = t370*t836;
- double t838 = t138*t110;
- double t846 = t1*t91;
- double t847 = t290*t846;
- double t850 = t2*t91;
- double t851 = t63*t850;
- double t854 = t371*t55;
- double t855 = t370*t854;
- double t856 = t41*t41;
- double t858 = t208*t110;
- double t864 = t98*t63;
- double t871 = t9*t91;
- double t873 = M*t87;
- double t874 = t139*t873;
- double t876 = t290*t98;
- double t879 = t98*t41;
- double t888 = t98*M;
- double t889 = t139*t888;
- double t892 = t152*t94;
- double t896 = t43*t8*t41;
- double t904 = 24.0*t351*t828*t832-16.0*t837*t403*t838-8.0*t372*t373*t138*t87-8.0*t289*t847+4.0*t289*t851-32.0*t855*t205*t856*t858+8.0*t402*t847-8.0*t53*t864-8.0*t314*eta*t87*t74+t385*t871-2.0*t874-8.0*t402*t876-8.0*t250*t252*t879+t181*t201*t91+4.0*t250*t393*t102+8.0*t147*t889-8.0*t147*t892-8.0*t896*t55*t110*t2+4.0*t250*t280*t888;
- double t905 = t219*t102;
- double t912 = t17*t87;
- double t921 = t87*t41;
- double t929 = t209*t879;
- double t937 = t1*t115;
- double t938 = t238*t937;
- double t941 = t2*t115;
- double t942 = t238*t941;
- double t945 = t41*t55;
- double t954 = t351*t856;
- double t956 = t336*t110;
- double t963 = -12.0*t218*t905+8.0*t218*t456*t235*t91-2.0*t159*t912+4.0*t188*t99+4.0*t188*t103-8.0*t289*t876-8.0*t207*t209*t921+4.0*t218*t892+8.0*t147*t905-16.0*t147*t929-4.0*t284*t252*t921-4.0*t137*t874+8.0*t348*t938+4.0*t353*t942-8.0*t334*t945*t337*t830-8.0*t366*t938+4.0*t363*t942-32.0*t954*t55*t144*t956-8.0*t438*t921*t59;
- double t972 = eta*t91;
- double t976 = t57*t55;
- double t979 = t208*t32;
- double t984 = r*t87;
- double t988 = t92*t17;
- double t1009 = t3*t91;
- double t1013 = t170*t873;
- double t1020 = t8*t91;
- double t1024 = t43*t32;
- double t1026 = t106*t1024*t87;
- double t1029 = -8.0*t237*t938-4.0*t250*t310*t94+8.0*t218*t929+2.0*t326*t327*t972-64.0*t180*t976*t856*t979*t111+t228*t972-2.0*t196*t15*t984-4.0*t214*t988-4.0*t320*t321*t972-4.0*t452*t88*t63+4.0*t402*t988-12.0*t402*t851-8.0*t219*t52*t828*t111-8.0*t302*t8*t87*t47+2.0*t163*t164*t1009+4.0*t265*t1013-8.0*t466*t274*t235*t87+4.0*t261*t1020*t41+8.0*t402*t1026;
- double t1030 = t976*t235;
- double t1031 = t145*t138;
- double t1033 = t809*t111;
- double t1036 = t336*t87;
- double t1037 = t290*t1036;
- double t1045 = t235*t108;
- double t1047 = t110*t1;
- double t1048 = t1047*t58;
- double t1049 = t238*t1048;
- double t1052 = t810*t945;
- double t1053 = eta*t110;
- double t1054 = t1053*t37;
- double t1057 = t138*t51;
- double t1058 = t235*t55;
- double t1060 = t1053*t442;
- double t1063 = t180*t836;
- double t1071 = t346*t1030;
- double t1077 = t1020*M;
- double t1094 = t37*t912;
- double t1103 = -32.0*t1030*t1031*t1033-8.0*t163*t1037-2.0*t294*t280*t873+t298*t299*t1009-48.0*t346*t1045*t1049+16.0*t1052*t1054-32.0*t1057*t1058*t1060-16.0*t1063*t456*t235*t110+4.0*t335*t337*t88+64.0*t1071*t1049+24.0*t362*t828*t832-4.0*t256*t1077-8.0*t214*t1026-8.0*t488*eta*t41*t112+4.0*t214*t851-48.0*t234*t1045*t1049-8.0*t218*t461*t98+4.0*t214*t1094+32.0*t1031*t1058*t337*t1047-4.0*t175*t95;
- double t1108 = t129*(t904+t963+t1029+t1103)*t631/2.0;
- double t1110 = t55*t87;
- double t1111 = t1110*t2;
- double t1112 = r*t110;
- double t1116 = t63*t1047;
- double t1122 = t110*t22;
- double t1126 = t110*t57;
- double t1127 = t813*r;
- double t1131 = t976*t115;
- double t1132 = t1131*t17;
- double t1139 = t976*t87;
- double t1143 = t2*t108;
- double t1144 = t58*t87;
- double t1147 = t22*t108;
- double t1148 = t115*t43;
- double t1151 = t108*t58;
- double t1152 = t43*t87;
- double t1158 = t52*t110;
- double t1161 = t249*t1151;
- double t1162 = t139*t94;
- double t1165 = -t1111+16.0*t720*t1112*t589+24.0*t707*t1116+16.0*t724*t838*t589-4.0*t9*t1122*t32-12.0*t697*t1126*t1127-2.0*t697*t1132+4.0*t249*t496*t1110*t17+4.0*t562*t1139*t1127+t520*t1143*t1144-t538*t1147*t1148+t776*t1151*t1152-4.0*t677*t109*t937+4.0*t1158*t682-4.0*t1161*t1162;
- double t1166 = t1147*t115;
- double t1168 = t9*t110;
- double t1172 = t138*t57;
- double t1176 = t146*t1151;
- double t1177 = t846*t63;
- double t1180 = t108*t115;
- double t1181 = t52*t1180;
- double t1184 = t110*t32;
- double t1189 = t9*t1180;
- double t1192 = t2*eta;
- double t1195 = t51*t110*t136;
- double t1198 = t209*t102;
- double t1201 = t43*t110;
- double t1202 = t558*t58;
- double t1213 = t8*t110;
- double t1214 = t1213*t136;
- double t1217 = t850*t17;
- double t1220 = t1*t57;
- double t1225 = t146*t108;
- double t1226 = t182*t91;
- double t1228 = -t520*t1166+4.0*t1168*t769-32.0*t146*t245*t1172*t111+4.0*t1176*t1177-2.0*t791*t1181-16.0*t751*t9*t1184-2.0*t509*t2*t1189-8.0*t17*t1192*t1195+4.0*t1161*t1198-16.0*t677*t1201*t1202-16.0*t646*t858*t1202-16.0*t707*t290*t110-8.0*t509*t1192*t1214-4.0*t1176*t1217+40.0*t677*t1201*t1220*t58+t1225*t1226;
- double t1237 = t976*t58;
- double t1238 = t146*t1237;
- double t1242 = t205*t87;
- double t1243 = t1242*t63;
- double t1246 = t37*t17;
- double t1251 = t373*t838;
- double t1258 = t51*t976;
- double t1259 = t809*t1258;
- double t1260 = t1144*t17;
- double t1263 = t138*t108;
- double t1272 = t43*t976;
- double t1276 = r*t108;
- double t1283 = t17*t830;
- double t1285 = -16.0*t107*t702*t111-4.0*t1161*t208*t87*t47+2.0*t1238*t1217-4.0*t180*t835*t1243+16.0*t1168*t1246-4.0*t1176*t864-16.0*t466*t1251-4.0*t809*t8*t55*t99-4.0*t1259*t1260+4.0*t724*t1263*t941-4.0*t1238*t1177-4.0*t707*t63*t1110-4.0*t677*t1272*t1144+4.0*t720*t1276*t941+4.0*t677*t1272*t937-4.0*t1283;
- double t1287 = t467*t921;
- double t1290 = t208*t108;
- double t1298 = t110*t56;
- double t1305 = t9*t55;
- double t1309 = t9*t108;
- double t1310 = t22*t115;
- double t1311 = t1310*t43;
- double t1315 = t52*t108;
- double t1318 = t52*t976;
- double t1319 = t941*t17;
- double t1331 = t164*t92;
- double t1333 = -4.0*t146*t835*t1287-4.0*t646*t1290*t937-4.0*t520*t1122*t136-4.0*t249*t745*t1298*t164+2.0*t249*t820*t110+2.0*t1305*t37*t87+t1309*t1311-t1309*t726*t1152-t1315*t726*t87+2.0*t1318*t1319+2.0*t1122+12.0*t52*t830*t604-12.0*t707*t1283-t707*t1111+t52*t1166+t249*t108*t1331;
- double t1338 = t631/t55;
- double t1340 = t17*a*t129*(t1165+t1228+t1285+t1333)*t1338;
- double t1342 = t197*t1;
- double t1351 = r*t2;
- double t1356 = t9*t43;
- double t1360 = t616*t64;
- double t1362 = t558*t699;
- double t1373 = -t2+t1342+t9*t37-4.0*t583*t586-3.0*t492*t609-t52*t589-4.0*t53*t604+t9*t1351*t23-t796*t442*t18-2.0*t1356*t684*M-t760*t1360+t760*t1362-t772*t1360+t772*t1362-2.0*t779*t1220*t703+4.0*t1356*t148+4.0*t779*t814;
- double t1376 = t7*t14*t634*t56*t1373;
- double t1381 = t830*t32;
- double t1408 = t592*t87;
- double t1417 = -2.0*t830+t1110*t1+2.0*t9*t1381-4.0*t1168*t442*t17-4.0*t1168*t617-4.0*t1158*t589-12.0*t52*t1047*t604+t9*t55*t2*t91-t1305*t442*t87-2.0*t1305*t846*t17-t1309*t941*t43+t1309*t592*t1152-t52*t1143*t115+t1315*t1408-2.0*t1318*t937*t17+4.0*t1305*t99+4.0*t1318*t1260;
- double t1420 = t86*M*a*r*t55*t1417;
- double t1421 = 1/t1;
- double t1425 = deltadr; // diff(Delta(r),r);
- double t1436 = dhrrdr; // diff(hrr(r,theta),r);
- double t1449 = dhrrdth; // diff(hrr(r,theta),theta);
- double t1452 = t87*t5+2.0*t9*t11*t87+t9*t2*t1449;
- double t1457 = t1421*t14;
- double t1459 = t1457*t1452/2.0;
- double t1463 = dhaadr; // diff(haa(r,theta),r);
- double t1466 = t18+2.0*t9*t82*t18+t9*t2*t1463;
- double t1469 = t1466*t85*t1421/2.0;
- double t1470 = t634*t56;
- double t1472 = t146*t352;
- double t1473 = t233*t32;
- double t1492 = t370*t57;
- double t1513 = t1492*t412*t197+4.0*t214*t708*t148-t214*t1351*t33+t181*t802-4.0*t411*t412*t17+4.0*t466*t665+t181*t182*t32-4.0*t214*t1246+4.0*t218*t732+t174*t191-t130;
- double t1515 = t180*t352;
- double t1522 = t138*t32;
- double t1530 = t8*t56;
- double t1559 = r*t32;
- double t1567 = t43*t23;
- double t1575 = -t370*t57*t205*t22-t133*t583+4.0*t265*t546*t813+t152*t386-t265*t170*t18-t188*t1559*t18+t174*eta*r*t23-4.0*t489*t604-2.0*t188*t1567*M+4.0*t438*t814+4.0*t302*t421;
- double t1580 = t145*t22;
- double t1585 = t180*t183;
- double t1590 = t204*t64;
- double t1603 = t761*t64*t233;
- double t1609 = t180*t37;
- double t1612 = t251*t56;
- double t1613 = t1612*t354;
- double t1626 = t51*t56;
- double t1641 = -4.0*t697*t65*t650-4.0*t1609*t704+2.0*t724*t1613-r*t144*t179*t745*t639-2.0*t261*t258+2.0*t280*eta*t1530*t699+4.0*t265*t1626*t699+4.0*t466*t658+8.0*t147*t209*t148+8.0*t207*t209*t140-2.0*t147*t139*t33;
- double t1651 = t180*t57;
- double t1652 = t205*t43;
- double t1661 = t2*t18;
- double t1668 = t249*t57;
- double t1685 = t146*t57;
- double t1695 = t205*t251;
- double t1706 = t298*t58*t233*t24-t250*t280*t33-2.0*t250*t393*t27+3.0*t1685*t274*t1661-3.0*t298*t299*t745+4.0*t250*t280*t183+t1668*t1695*t22+t1685*t467*t22+4.0*t163*t670*t500+t159*t197+2.0*t489*t700;
- double t1712 = t1470*t129*(-8.0*t218*t139*t183+4.0*t250*t252*t148-t1651*t1652*t22+t133-2.0*t163*t164*t745+t1668*t205*t208*t138*t1661+4.0*t1472*t1473*t699+4.0*t1515*t1522*t239+4.0*t1515*t1522*t699-4.0*t574*t1590*t670+3.0*t1651*t205*t138*t1661-4.0*t1515*t1024*t592+4.0*t1472*t979*t592+4.0*t1472*t1473*t239+4.0*t284*t252*t140+t1706+4.0*t273*t274*t15-4.0*t163*t63*t496-4.0*t147*t732+4.0*t402*t689-4.0*t188*t742+4.0*t720*t748+4.0*t372*t671-4.0*t372*t788+2.0*t326*t322+2.0*t389*eta*t1530*t58+4.0*t314*eta*t43*t814-2.0*t1580*eta*t56*t58+4.0*t452*t709-4.0*t402*t685+4.0*t289*t685-2.0*t214*t689+4.0*t289*t737-4.0*t289*t806-t538*t1603+t1641+2.0*t163*t635+4.0*t53*t817-4.0*t218*t643+t1575-2.0*t520*t774+t1513+2.0*t1585*t721+t139*t18)*t631;
- double t1718 = t146*t745;
- double t1723 = t3*t56;
- double t1724 = t1723*t64;
- double t1727 = t509*t22;
- double t1731 = -4.0*t596*t354*t63-2.0*r*t3+4.0*t1718*t65*t509+4.0*t134+t158+t525*t1724-8.0*t172+4.0*t1727*t640+t213+4.0*t221+t226;
- double t1736 = -12.0*t514*t343+t242+t248+t268+t278+16.0*t282+t287+t293-t340+8.0*t344-t350;
- double t1748 = t180*t745;
- double t1752 = -12.0*t356-12.0*t364+t368+t377+t384-16.0*t391+4.0*t525*t22*t57*t813+t538*t1723*t64*t208-t401+4.0*t1748*t65*t17-t407;
- double t1778 = t208*t51;
- double t1779 = t1778*t41;
- double t1780 = t57*eta;
- double t1781 = t1780*t354;
- double t1784 = t334*t41;
- double t1791 = -8.0*t720*t774-32.0*t677*t1172*t726-4.0*t1609*t59*t160+4.0*t538*t1723*t515+2.0*t520*t1723*t64*t43+2.0*t557*t761*M+8.0*t1609*t288*t54-8.0*t574*t204*t18*t598+4.0*t1779*t1781+4.0*t1784*t1781-4.0*t1585*t715+8.0*t677*t748;
- double t1797 = t325*t8;
- double t1800 = t180*t47;
- double t1805 = t699*t63;
- double t1808 = t17*t22;
- double t1814 = t529*t22;
- double t1821 = -t415+8.0*t809*t1626*t307+2.0*t1797*t785+4.0*t1800*t721+t425+t427+8.0*t809*t145*t204*t1805+2.0*t1808*t195*t639+4.0*t646*t1613+2.0*t1814*t652+16.0*t1057*t41*t1780*t726;
- double t1840 = t3*t64;
- double t1843 = t22*t64;
- double t1853 = 4.0*t1609*t1590*t63-4.0*t724*t1603+2.0*t9*t32*t3*r+t431+12.0*t1718*t59*t637-4.0*t697*t59*t374*M-8.0*t341*t416-t492*t1840*t208-4.0*t591*t1843*t17-8.0*t596*t726*t54-4.0*t514*t1843*t509;
- double t1856 = t515*t140;
- double t1879 = t699*t17;
- double t1882 = 4.0*t52*t780*t1856-t195*t1724-4.0*t492*t201*t138-2.0*t341*t1840*t43-4.0*t591*t359-4.0*t341*t201*r+4.0*t520*t1723*t58*r-2.0*t625*t325*t197+4.0*t195*t780*t1879-t437-t445;
- double t1888 = 4.0*t446-t451+t455-t460+t464+t470+t474-2.0*t325*t130-16.0*t481+8.0*t494-t499+t503;
- double t1894 = t129*(t1731+t1736+t1752+t1791+t1821+t1853+t1882+t1888)*t631/2.0;
- double t1901 = dhaadth; // diff(haa(r,theta),theta);
- double t1917 = t43*t336;
- double t1942 = t146*t828;
- double t1946 = M*t110;
- double t1947 = t1946*t32;
- double t1948 = t139*t1947;
- double t1955 = t180*t1237;
- double t1968 = -t321*t87-t159*t87-t181*t1226+t525*t761*t115+4.0*t147*t1162+8.0*t146*t945*t1917*t1047+4.0*t697*t116*t509-2.0*t1585*t698*t941-4.0*t720*t725*t941-4.0*t163*t63*t1036-4.0*t289*t1177-4.0*t289*t864-4.0*t372*t1243-4.0*t678*eta*t1013-32.0*t1942*t979*t1048+16.0*t1176*t1948-32.0*t180*t828*t1024*t1048+24.0*t1955*t63*t1047*t32+4.0*t574*t204*t115*t63-2.0*t724*t233*t56*t941;
- double t1971 = t139*t52;
- double t1977 = t321*eta;
- double t1980 = t976*t41;
- double t2003 = t55*t58;
- double t2005 = t830*t742;
- double t2008 = t976*t205;
- double t2015 = t55*M;
- double t2017 = t1351*t110;
- double t2022 = t314*t1780;
- double t2034 = -4.0*t466*t1287+2.0*t180*t55*t182*t1184-4.0*t180*t2003*t2005-4.0*t370*t2008*t1283+2.0*t520*t761*t1148-4.0*t2015*t8*t2017-4.0*t53*t99-4.0*t2022*t1260-2.0*t489*t136*t87-8.0*t488*t1053*t1151*t17+t187*t191*t87;
- double t2046 = t51*r;
- double t2069 = t146*t2003;
- double t2089 = t2*t87;
- double t2102 = -4.0*t1977*t1626*t1144+2.0*t188*t95-16.0*t855*t1251-4.0*t1472*t979*t937+t250*t219*t98+2.0*t250*t280*t94-t1668*t1695*t2089-3.0*t1685*t467*t2089-t298*t299*t92-2.0*t163*t1331+2.0*t147*t321*t98;
- double t2117 = t115*t208;
- double t2133 = t249*t2003;
- double t2162 = 2.0*t2133*t389*t1184-4.0*t214*t88*t742-4.0*t452*t89+16.0*t180*t1151*t2005+t181*t726*t98+2.0*t214*t1217-2.0*t326*t1351*t972-4.0*t2133*t280*t1947-4.0*t146*t2008*t280*t1946+2.0*t265*t1077-t174*t972;
- double t2168 = t1470*r*t129*(-8.0*t1971*t110*t108*t813+t1977*t170*t87-16.0*t1980*t334*t1033-4.0*t250*t456*t888-3.0*t1651*t1652*t2089-8.0*t180*t2008*t139*t1946-32.0*t180*t1030*t1522*t111-16.0*t146*t55*t290*t956-16.0*t837*t1116-16.0*t1063*t209*t41*t110+t538*t761*t2117-8.0*t207*t678*t873-8.0*t147*t678*t888+4.0*t2069*t133*t1184-4.0*t284*t456*t873-t1492*t412*t87+4.0*t1609*t116*t17+4.0*t2015*t2046*t1054-4.0*t1515*t1024*t1144-4.0*t1515*t1024*t937-4.0*t1472*t979*t1144-2.0*t261*t1530*t1144+4.0*t218*t1198+t2034+t1968-8.0*t2069*t1948-16.0*t1052*t1060-4.0*t678*t52*t57*t87*t813+t2102-t133*t871+t2162-4.0*t402*t1217-4.0*t218*t1162+4.0*t402*t1177)*t631;
- double t2169 = t3*t108;
- double t2180 = t108*M;
- double t2181 = t2180*t8;
- double t2190 = t835*t41;
- double t2199 = t385*eta;
- double t2203 = t976*eta;
- double t2204 = t2203*t941;
- double t2212 = 2.0*t520*t2169*t1148+4.0*t181*t201*t1184-2.0*t385*t110+t538*t2169*t2117+2.0*t2181*t1351*t87-4.0*t1580*eta*t1132+8.0*t1225*t1037-4.0*t2190*t145*t321*eta*t115-8.0*t175*t1184*t17+2.0*t2199*t1213*t32+4.0*t1779*t2204+2.0*t1808*t195*t1180+4.0*t1727*t1181;
- double t2226 = t208*t3;
- double t2227 = t2226*eta;
- double t2238 = t138*t369;
- double t2241 = t854*t144*t1242;
- double t2258 = 32.0*t954*t380*t956+32.0*t208*t369*t856*t371*t56*t144*t205*t110+4.0*t509*t1122-4.0*t2227*t1214-8.0*t2199*t1195-4.0*t256*t1258*t115*M+2.0*t1814*t1189+8.0*t2238*t235*t2241-2.0*t8*t3*t110-8.0*t256*t1213*t183+8.0*t583*t521*t830+8.0*t557*t63*t830+4.0*t1784*t2204;
- double t2260 = t233*t179;
- double t2274 = t208*t179;
- double t2284 = t1053*t726;
- double t2299 = t342*t1112*t32;
- double t2304 = 8.0*t2260*t235*t2241-2.0*t2199*t51*t108*t115+8.0*t896*t1298*t2-t2227*t8*t108*t115+64.0*t2274*t856*t204*t238*t111-4.0*t1942*t1917*t88+32.0*t1778*t352*t2284+4.0*t1238*t905-8.0*t720*t1263*t1310+4.0*t1800*t109*t941-4.0*t1585*t1276*t1310+24.0*t402*t2299+4.0*t1748*t1132;
- double t2314 = t180*t835*t58;
- double t2322 = t152*t1947;
- double t2346 = 4.0*t1609*t835*t115*t63-4.0*t724*t233*t108*t1310-8.0*t2314*t1026-72.0*t1515*t1024*t831+8.0*t2314*t847+24.0*t218*t2322-16.0*t214*t2299-4.0*t1238*t889+8.0*t146*t319*t1917*t830+32.0*t677*t208*t56*t831+8.0*t2190*t334*t809*t1144+4.0*t1718*t1131*t509+t525*t2169*t115;
- double t2366 = t234*t1030;
- double t2367 = t238*t1144;
- double t2378 = t22*eta;
- double t2391 = -72.0*t1472*t979*t831-4.0*t1955*t1094+32.0*t289*t63*t1381+16.0*t646*t1612*t831+32.0*t1031*t347*t1033+8.0*t677*t1290*t941+8.0*t2366*t2367-24.0*t152*t52*t1126*t813-32.0*t319*t810*t1054+8.0*t325*t2046*t2378*t1184+4.0*t488*t2203*t1260-24.0*t1580*t1053*t604+4.0*t1971*t1139*t813;
- double t2392 = t56*t235;
- double t2398 = t145*t3;
- double t2409 = t1213*t22;
- double t2432 = t235*t371;
- double t2434 = t144*t205;
- double t2435 = t2434*t1047;
- double t2442 = -32.0*t146*t2392*t138*t336*t1047-t2398*eta*t108*t115-8.0*t1797*t327*t110-4.0*t2398*eta*t1298*t58+4.0*t17*t2409+2.0*t228*t1053*t32+8.0*t2366*t938+8.0*t17*t2378*t145*t56*t111+16.0*t509*t2378*t1195+8.0*t529*t2378*t1214+16.0*t1800*t43*t56*t831+16.0*t2238*t2432*t2435+4.0*t646*t251*t108*t941;
- double t2448 = t144*t58*t846;
- double t2463 = t2434*t88;
- double t2485 = 32.0*t1057*t2392*t1060-8.0*t2366*t2448+16.0*t2260*t2432*t2435+8.0
- *t1071*t2367+8.0*t1071*t938+32.0*t334*t352*t2284+4.0*t43*t369*t2190*t2463-8.0*t1071*t2448+8.0*t2274*t2190*t2463+4.0*t251*t145*t2190*t2463+4.0*t1955*t851+8.0*t828*t810*t809*t98-2.0*t2180*t2046*t1192*t98;
- double t2506 = t180*t835*t235;
- double t2513 = t180*t1980;
- double t2520 = t146*t1980;
- double t2531 = -32.0*t204*t41*t334*t2284+48.0*t366*t1049+48.0*t237*t1049-32.0*t147*t2322-16.0*t250*t310*t1947+8.0*t147*t385*t1184+4.0*t250*t2226*t1184+8.0*t2506*t1522*t1144-8.0*t2506*t1522*t937+8.0*t2513*t1024*t1408-12.0*t2513*t1024*t941+8.0*t2520*t979*t1408-12.0*t2520*t979*t941-64.0*t180*t347*t1522*t1048;
- double t2537 = t129*(t2212+t2258+t2304+t2346+t2391+t2442+t2485+t2531)*t1338/2.0;
- double t2589 = 2.0*t327+2.0*t325*t159-2.0*t1797*t1342+8.0*t341*t106*t1559+4.0*t341*t106*t1567+t492*t1843*t208+4.0*t492*t182*t138+2.0*t341*t1843*t43+4.0*t341*t182*r+4.0*t514*t354*t509+12.0*t514*t726*t637-4.0*t52*t1220*t1856+t195*t762+4.0*t591*t354*t17-4.0*t2022*t1879+4.0*t591*t726*M+4.0*t596*t239*t63+8.0*t596*t592*t54-8.0*t341*t307-8.0*t596*t1805;
- double t2625 = 2.0*t1201*t22+2.0*t2409+8.0*t1797*t2017-2.0*t2181*t984*t1+16.0*t52*t1298*t806+4.0*t492*t1122*t299+8.0*t341*t1122*t164+24.0*t52*t1126*t674+4.0*t358*t1122*t58+24.0*t195*t1126*t726*t17+32.0*t195*t204*t110*t592*t63;
- double t2646 = t195*t835;
- double t2655 = 4.0*t1315*t1177+t1309*t1310*t208+2.0*t1315*t1311+4.0*t1318*t941*t509-4.0*t1259*t515*t873+t195*t1166+4.0*t195*t976*t1319-4.0*t195*t976*t1*t1260+
- 4.0*t2646*t937*t63-8.0*t1315*t864-8.0*t2646*t1144*t63;
- christoffel[0][0][0] = 0.0;
- christoffel[0][0][1] = -t7*t14*t77/2.0;
- christoffel[0][0][2] = -t86*(-2.0*t89+t9*t92-4.0*t26*t95+4.0*t31*t99+4.0*t31*t103+16.0*t107*t112+4.0*t53*t63*t116-8.0*t9*t87*t70-8.0*t52*t87*t74)/2.0;
- christoffel[0][0][3] = 0.0;
- christoffel[0][1][0] = t633;
- christoffel[0][1][1] = 0.0;
- christoffel[0][1][2] = 0.0;
- christoffel[0][1][3] = t827;
- christoffel[0][2][0] = t1108;
- christoffel[0][2][1] = 0.0;
- christoffel[0][2][2] = 0.0;
- christoffel[0][2][3] = t1340;
- christoffel[0][3][0] = 0.0;
- christoffel[0][3][1] = -t1376;
- christoffel[0][3][2] = -t1420;
- christoffel[0][3][3] = 0.0;
- christoffel[1][0][0] = t633;
- christoffel[1][0][1] = 0.0;
- christoffel[1][0][2] = 0.0;
- christoffel[1][0][3] = t827;
- christoffel[1][1][0] = 0.0;
- christoffel[1][1][1] = t1421/t5*t14*(t18*t6-t1*t1425*t5+2.0*t31*t10*t18*t5-2.0*t9*t2*t10*t1425+t9*t2*t1436*t5)/2.0;
- christoffel[1][1][2] = -t1421*t85*t1452/t6/2.0;
- christoffel[1][1][3] = 0.0;
- christoffel[1][2][0] = 0.0;
- christoffel[1][2][1] = t1459;
- christoffel[1][2][2] = t1469;
- christoffel[1][2][3] = 0.0;
- christoffel[1][3][0] = t1712;
- christoffel[1][3][1] = 0.0;
- christoffel[1][3][2] = 0.0;
- christoffel[1][3][3] = t1894;
- christoffel[2][0][0] = t1108;
- christoffel[2][0][1] = 0.0;
- christoffel[2][0][2] = 0.0;
- christoffel[2][0][3] = t1340;
- christoffel[2][1][0] = 0.0;
- christoffel[2][1][1] = t1459;
- christoffel[2][1][2] = t1469;
- christoffel[2][1][3] = 0.0;
- christoffel[2][2][0] = 0.0;
- christoffel[2][2][1] = -t6*t1466*t1457/2.0;
- christoffel[2][2][2] = (t87+2.0*t9*t82*t87+t9*t2*t1901)*t1421*t85/2.0;
- christoffel[2][2][3] = 0.0;
- christoffel[2][3][0] = -t2168;
- christoffel[2][3][1] = 0.0;
- christoffel[2][3][2] = 0.0;
- christoffel[2][3][3] = t2537;
- christoffel[3][0][0] = 0.0;
- christoffel[3][0][1] = -t1376;
- christoffel[3][0][2] = -t1420;
- christoffel[3][0][3] = 0.0;
- christoffel[3][1][0] = t1712;
- christoffel[3][1][1] = 0.0;
- christoffel[3][1][2] = 0.0;
- christoffel[3][1][3] = t1894;
- christoffel[3][2][0] = -t2168;
- christoffel[3][2][1] = 0.0;
- christoffel[3][2][2] = 0.0;
- christoffel[3][2][3] = t2537;
- christoffel[3][3][0] = 0.0;
- christoffel[3][3][1] = -t7*t14*t56*t2589/2.0;
- christoffel[3][3][2] = -t86*t55*(t2625+t2655)/2.0;
- christoffel[3][3][3] = 0.0;
- return true;
- }
| Il faut dire que les formules mathématiques dont c'est tiré sont particulièrement gratinées... ---------------
Les aéroports où il fait bon attendre, voila un topic qu'il est bien
|