(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 138120, 3665] NotebookOptionsPosition[ 124205, 3287] NotebookOutlinePosition[ 124547, 3302] CellTagsIndexPosition[ 124504, 3299] WindowFrame->Normal ContainsDynamic->False*) (* Beginning of Notebook Content *) Notebook[{ Cell["\<\ TetrGaussRuleInfo [ { rule_, numer_ }, point_ ] := Module [ { jk6 = {{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}}, jk12= {{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}, {2,1},{3,1},{4,1},{3,2},{4,2},{4,3}}, i = point, j, k, g1, g2, g3, g4, h1, w1, w2, w3, eps=10.^(-16), info = {{Null,Null,Null,Null}, 0} }, If [ rule == 1, info = {{1/4,1/4,1/4,1/4},1}]; If [ rule == 4, g1 = (5-Sqrt[5])/20; h1=(5+3*Sqrt[5])/20; info={{g1,g1,g1,g1},1/4}; info[[1,i]]=h1]; If [ rule == 8, j= i - 4; g1=(55-3*Sqrt[17]+Sqrt[1022-134*Sqrt[17]])/196; g2=(55-3*Sqrt[17]-Sqrt[1022-134*Sqrt[17]])/196; w1=1/8+Sqrt[(1715161837-406006699*Sqrt[17])/23101]/3120; w2=1/8-Sqrt[(1715161837-406006699*Sqrt[17])/23101]/3120; If [ j <= 0, info={{g1,g1,g1,g1},w1}; info[[1,i]]=1-3*g1]; If [ j > 0, info={{g2,g2,g2,g2},w2}; info[[1,j]]=1-3*g2]]; If [ rule == -8, j=i-4; If [ j <= 0, info={{0,0,0,0}, 1/40}; info[[1,i]]=1]; If [ j > 0, info={{1,1,1,1}/3, 9/40}; info[[1,j]]=0]]; If [ rule==14, g1 = 0.09273525031089122640232391373703060; g2 = 0.31088591926330060979734573376345783; g3 = 0.45449629587435035050811947372066056; If [ !numer, {g1,g2,g3}=Rationalize[{g1,g2,g3},eps]]; w1=(-1+6*g2*(2+g2*(-7+8*g2))+14*g3-60*g2*(3+4*g2* (-3+4*g2))*g3+4*(-7+30*g2*(3+4*g2*(-3+4*g2)))*g3^2)/ (120*(g1-g2)*(g2*(-3+8*g2)+6*g3+8*g2*(-3+4*g2)*g3-4* (3+4*g2*(-3+4*g2))*g3^2+8*g1^2*(1+12*g2* (-1+2*g2)+4*g3-8*g3^2)+g1*(-3-96*g2^2+24*g3*(-1+2*g3)+ g2*(44+32*(1-2*g3)*g3)))); w2=(-1-20*(1+12*g1*(2*g1-1))*w1+20*g3*(2*g3-1)*(4*w1-1))/ (20*(1+12*g2*(2*g2-1)+4*g3-8*g3^2)); If [ i<5, info={{g1,g1,g1,g1},w1}; info[[1,i]] =1-3*g1]; If [ i>4&&i<9, info={{g2,g2,g2,g2},w2}; info[[1,i-4]]=1-3*g2]; If [ i > 8, info={{g3,g3,g3,g3},1/6-2*(w1+w2)/3}; {j,k}=jk6[[i-8]]; info[[1,j]]=info[[1,k]]=1/2-g3] ]; If [ rule == -14, g1=(243-51*Sqrt[11]+2*Sqrt[16486-9723*Sqrt[11]/2])/356; g2=(243-51*Sqrt[11]-2*Sqrt[16486-9723*Sqrt[11]/2])/356; w1=31/280+Sqrt[(13686301-3809646*Sqrt[11])/5965]/600; w2=31/280-Sqrt[(13686301-3809646*Sqrt[11])/5965]/600; If [ i<5, info={{g1,g1,g1,g1},w1}; info[[1,i]] =1-3*g1]; If [ i>4&&i<9, info={{g2,g2,g2,g2},w2}; info[[1,i-4]]=1-3*g2]; If [ i>8&&i<15, info={{0,0,0,0},2/105}; {j,k}=jk6[[i-8]]; info[[1,j]]=info[[1,k]]=1/2] ]; If [ rule == 15, g1=(7-Sqrt[15])/34; g2=7/17-g1; g3=(10-2*Sqrt[15])/40; w1=(2665+14*Sqrt[15])/37800; w2=(2665-14*Sqrt[15])/37800; If [i<5, info={{g1,g1,g1,g1},w1};info[[1,i]]=1-3*g1]; If [i>4&&i<9, info={{g2,g2,g2,g2},w2};info[[1,i-4]]=1-3*g2]; If [i>8&&i<15,info={{g3,g3,g3,g3},10/189}; {j,k}=jk6[[i-8]]; info[[1,j]]=info[[1,k]]=1/2-g3]; If [i==15,info={{1/4,1/4,1/4,1/4},16/135}] ]; If [ rule==-15, g1=(13-Sqrt[91])/52; If [i<5, info={{1,1,1,1}/3,81/2240};info[[1,i]]=0]; If [i>4&&i<9, info={{1,1,1,1}/11,161051/2304960}; info[[1,i-4]]=8/11]; If[i>8&&i<15, info={{g1,g1,g1,g1},338/5145}; {j,k}=jk6[[i-8]]; info[[1,j]]=info[[1,k]]=1/2-g1]; If [i==15,info={{1/4,1/4,1/4,1/4},6544/36015}] ]; If [ rule == 24, g1 = 0.214602871259915202928839219386284991; g2 = 0.040673958534611353115579448956410059; g3 = 0.322337890142275510343994470762492125; If [ !numer, {g1,g2,g3}=Rationalize[{g1,g2,g3},eps]]; w1 = (85+2*g2*(-319+9*Sqrt[5]+624*g2)-638*g3- 24*g2*(-229+472*g2)*g3+96*(13+118*g2*(-1+2*g2))*g3^2+ 9*Sqrt[5]*(-1+2*g3))/(13440*(g1-g2)*(g1-g3)*(3-8*g2+ 8*g1*(-1+2*g2)-8*g3+16*(g1+g2)*g3)); w2 = -(85+2*g1*(-319+9*Sqrt[5]+624*g1)-638*g3- 24*g1*(-229+472*g1)*g3+96*(13+118*g1*(-1+2*g1))*g3^2+ 9*Sqrt[5]*(-1+2*g3))/(13440*(g1-g2)*(g2-g3)*(3-8*g2+ 8*g1*(-1+2*g2)-8*g3+16*(g1+g2)*g3)); w3 = (85+2*g1*(-319+9*Sqrt[5]+624*g1)-638*g2- 24*g1*(-229+472*g1)*g2+96*(13+118*g1*(-1+2*g1))*g2^2+ 9*Sqrt[5]*(-1+2*g2))/(13440*(g1-g3)*(g2-g3)*(3-8*g2+ 8*g1*(-1+2*g2)-8*g3+16*(g1+g2)*g3)); 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