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From: Hunter on 20 Dec 2009 07:22
Lisp developers are wanted for a project to build a Mathematica
emulator using the Maxima computer algebra system. Mockmma uses
wxMaxima to evaluate a small subset of commands in the syntax of
Mathematica (tm),
which is a trademark of Wolfram Research Incorporated (WRI). Mockmma
is in no way associated with WRI and is based on code written by
Richard Fateman in 1990 and
compatibility functions written by John Lapeyre.

To install Mockmma: unzip Mockmma.tar.gz (or checkout trunk/Mockmma
from the Mockmma sourceforge project) into the directory share\mockmma
under the Maxima source tree; type load("mockmma/mockmma.lisp"); and
type :lisp (mockmma). You should see the prompt "In[1] :=". To run a
test suite, enter batch("mockmma/rtest_mockmma.mac", 'test). You can
load Mockmma.wxm by choosing File, Open from the wxMaxima menu.

Below is a list of 200+ Mathematica (tm) commands which Mockmma
correctly emulates. Any help in developing Mockmma is welcome.

Mockmma is experimental. It has no error handling and may not work on
all platforms. No warranty is expressed or implied.

"PrimeQ[23] "
"2+3"
"3^7"
"4!"
"yy=5"
"yy^2"
"Sin[1.0]"
"5+1.0"
"2.3+5.63 "
"g[x_]:=x^3"
"g[2]"
"Map[g, {1,2,3}]=={1,8,27}"
"Sqrt[4]"
"Sqrt[3.0]"
"{1,4,9,16}[[3]]"
"Cos[0]"
"Sin[0]"
"Cos[Pi]"
"Sin[Pi]"
"Sin[Pi/2]"
"Cos[Pi/2]"
"2>1"
"2<1"
"2>1"
"1<2"
"2<=1"
"1>=2"
"2>=2"
"2<=2"
"FactorInteger[24]=={{2, 3}, {3, 1}}"
"Expand[(1+x)^2]==1+2*x+x^2"
"Log[E]"
"E==Exp[1]"
"I*I "
"D[Log[x],x]==1/x "
"D[Sin[x],x]==Cos[x] "
"D[Cos[x],x]==-Sin[x] "
"Factor[x^2+2*x+1]==(x+1)^2 "
"Integrate[x,x]==x^2 / 2"
"Integrate[Sin[z]*z,z]== - z Cos[z] + Sin[z]"
"Integrate[x,{x,0,1}]==1/2"
"True && True "
"True && False "
"True || False "
"False || False "
"{a,b}.{c,d}==a*c + b * d "
"{2,3}.{5,3}"
"If[True,a,b]==a "
"If[False,a,b]==b "
"If[False,a,b]==b "
"ArcSin[1]==Pi /2 "
"Abs[1]"
"Abs[-1]"
"Round[1.1]"
"Round[1.6]"
"Mod[13,3]"
"Mod[27,8]"
"Max[27,8]"
"Min[27,8]"
"Sign[27]"
"Sign[0]"
"Sign[-23]"
"Re[5+ 7 I]"
"Im[5+ 7 I]"
"Conjugate[5+ 7 I]==5 - 7 I "
"Floor[12.5]"
"Ceiling[12.5]"
"GCD[12,18]"
"LCM[12,18]"
"KroneckerDelta[12,18]"
"KroneckerDelta[a,a]"
"Table[1,{3}]=={1, 1,1} "
"Table[i^2,{i,1,10}]=={1, 4, 9, 16, 25, 36, 49, 64, 81, 100} "
"Table[i^2,{i,10}]=={1, 4, 9, 16, 25, 36, 49, 64, 81, 100} "
"Table[f[i], {i, 1, 3}]=={f[1],f[2],f[3]} ")
"Module[{i=0},Table[i++,{10}]]=={1, 2, 3, 4, 5, 6, 7, 8, 9, 10} ")
"Table[10*i + j, {i, 4},{j,3}]==Out[2]:= {{11, 12, 13}, {21, 22, 23},
{31, 32, 33}, {41, 42, 43}}"
"Table[100* i + 10* j + k, {i, 3}, {j, 2}, {k, 4}]==
{{{111, 112, 113, 114}, {121, 122, 123, 124}}, {{211, 212, 213, 214},
{221, 222, 223, 224}}, {{311, 312, 313, 314}, {321, 322, 323, 324}}}"
"Table[x^2, {x, {1, 4, 9, 16}}]=={1, 16, 81, 256}")
"Table[j^i, {i, {1, 2, 4}}, {j, {1, 4, 9}}]=={{1, 4, 9}, {1, 16, 81},
{1, 256, 6561}} "
"Take[{a,b,c,d,e,f},4]=={a,b,c,d}"
"Take[{a,b,c,d,e,f},-3]=={d,e,f}"
"Take[{a,b,c,d,e,f},{2,4}]=={b,c,d}"
"Take[{a,b,c,d,e,f},{2,-2}]=={b,c,d,e}"
"Take[{{11,12,13},{21,22,23},{31,32,33}},2]=={{11,12,13},{21,22,23}}"
"Take[{{11,12,13},{21,22,23},{31,32,33}},3,2]=={{11, 12}, {21, 22},
{31, 32}}"
"Take[{{11,12,13},{21,22,23},{31,32,33}},2,-1]=={{13}, {23}}"
"Take[Partition[Range[11,55],5],{2,4},{3,5}]=={{18, 19, 20}, {23, 24,
25}, {28, 29, 30}}"
"Partition[{a,b,c,d,e,f},2]=={{a, b}, {c, d}, {e, f}}"
"Partition[{a,b,c,d,e,f},3,1]=={{a, b, c}, {c, d, e}}"
"Fold[f,x,{a,b,c,d}]==f[f[f[f[x, a], b], c], d]"
"Fold[Times,1,{a,b,c,d}]==a b c d "
"Apply[f,{x}]==f[x]"
"Apply[Plus,{x,y,z}]== x + y + z "
"Apply[#1+#2&,{x,y}]==x+y "
"Fold[ x * #1 + #2 &, 0, {a, b, c, d, e}]==e + x (d + x (c + x (b + a
x)))"
"Reverse[{a,b,c,d}]=={d, c, b, a}"
"Fold[1/(#1 + #2)&, x, Reverse[{a, b, c, d}]]==1/(1/(1/(1/(x+d)+c)+b)
+a)"
"Fold[ 10*#1 + #2&, 0, {4, 5, 1, 6, 7, 8}]"
"Fold[#2-#1&, 0, Reverse[{a, b, c, d, e}]]==a - b + c - d + e "
"Fold[ {#2,#1}&, x, {a, b, c, d}]=={d, {c, {b, {a, x}}}}"
"Fold[Apply[#2,{#1}]&, x, {a,b,c,d}]==d[c[b[a[x]]]]"
"Fold[f[#]& , x, Range[5]]==f[f[f[f[f[x]]]]]"
"Union[{1,2},{3,4}]=={1, 2, 3, 4}"
"Join[{a,b,c},{x,y},{u,v,w}]=={a, b, c, x, y, u, v, w}"
"Join[{{a, b}, {c, d}}, {{1, 2}, {3, 4}}]=={{a, b}, {c, d}, {1, 2},
{3, 4}}"
"Union[{1, 2, 1, 3, 6, 2, 2}]=={1, 2, 3, 6}"
"Union[{a, b, a, c}, {d, a, e, b}, {c, a}]=={a, b, c, d, e}"
"Prepend[{a, b, c, d}, x]=={x, a, b, c, d}"
"Append[{a, b, c, d}, x]=={a, b, c, d, x}"
"Riffle[{a,b,c},{x,y,z}]=={a, x, b, y, c, z}"
"Fold[Union[#1, #1 + #2]&, {0}, {1, 2, 2, 8}]=={0, 1, 2, 3, 4, 5, 8,
9, 10, 11, 12, 13}"
"FoldList[f,x,{a,b,c,d}]=={x, f[x, a], f[f[x, a], b], f[f[f[x, a], b],
c], f[f[f[f[x, a], b], c], d]}"
"FoldList[Plus,0,{a,b,c,d}]=={0, a, a + b, a + b + c, a + b + c + d}"
"FoldList[#1^#2&,x,{a,b,c,d}]=={x, x^a , (x^a )^b , ((x^a )^b )^c ,
(((x^a )^b )^c )^d }"
"FoldList[#1*#2&,x,{a,b,c,d}]=={x, a x, a b x, a b c x, a b c d x}"
"FoldList[Times,1,Range[10]]=={1, 1, 2, 6, 24, 120, 720, 5040, 40320,
362880, 3628800}"
"FoldList[1/(#2 + #1)&, x, Reverse[{a, b, c}]]==Out[5]:= {x, (c + x)
^-1 , (b + (c + x)^-1 )^-1 , (a + (b + (c + x)^-1 )^-1 )^-1 }"
"Nest[f,x,3]==f[f[f[x]]]"
"Nest[(1 + #)^2& , 1, 3]==676"
"Nest[(1 + #)^2& , x, 5]==(1 + (1 + (1 + (1 + (1 + x)^2 )^2 )^2 )^2 )
^2"
"Nest[Sqrt,100.0,4]==1.333521432163324"
"Range[4]=={1, 2, 3, 4}"
"Range[x,x+4]=={x, 1 + x, 2 + x, 3 + x, 4 + x}"
"IntegerDigits[58127]=={5, 8, 1, 2, 7}"
"IntegerDigits[58127,2]=={1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1,
1}"
"IntegerDigits[58127,16]=={14, 3, 0, 15}"
"IntegerDigits[{6,7,2},2]=={{1, 1, 0}, {1, 1, 1}, {1, 0}}"
"IntegerDigits[7,{2,3,4}]=={{1, 1, 1}, {2, 1}, {1, 3}}"
"IntegerDigits[Range[0,7],2]=={{0}, {1}, {1, 0}, {1, 1}, {1, 0, 0},
{1, 0, 1}, {1, 1, 0}, {1, 1, 1}}"
"IntegerDigits[Range[0,7],2,3]=={{0, 0, 0}, {0, 0, 1}, {0, 1, 0}, {0,
1, 1}, {1, 0, 0}, {1, 0, 1}, {1, 1, 0}, {1, 1, 1}}"
"FromDigits[{5, 1, 2, 8}]==5128"
"FromDigits[{1, 0, 1, 1, 0, 1, 1}, 2]==91"
"FromDigits[{a, b, c, d, e}, x]==e + d x + c x^2 + b x^3 + a x^4"
"FromDigits[{7, 11, 0, 0, 0, 122}]==810122"
"Chop[10^-20]==0"
"Chop[a]==a "
"Chop[ 1 + 10.^-20* I - 7*(a + 10.^-30* b)*I]==1 - 7 I a "
"Chop[10^-17]==0"
"Chop[-1]==-1"
"Chop[-10.^-17]==0"
"Chop[{1,10^-20}]=={1, 0}"
"Chop[{10^-20,{1,10^-17}}]=={0, {1, 0}}"
"Chop[1+I]==1+I "
"Chop[1+10.^-20 I]==1 "
"Chop[10^-20 +I]==I "
"Dimensions[{{a, b, c}, {d, e, f}}]=={2, 3}"
"Dimensions[f[f[x, y], f[a, b], f[s, t]]]=={3, 2}"
"Dimensions[f[g[x, y], g[a, b], g[s, t]]]=={3, 2}"
"Most[Range[10]]=={1, 2, 3, 4, 5, 6, 7, 8, 9}"
"Dimensions[{{a, b, c}, {d, e, f}}]=={2, 3}"
"Det[{{1,2,3},{4,5,6},{7,8,9}}]==0"
"Transpose[{{1,2,3},{4,5,6},{7,8,9}}]=={{1, 4, 7}, {2, 5, 8}, {3, 6,
9}}"
"Det[ {{a,b},{c,d}}]== -(1 b c) + a d "
"Tr[{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}]==15"
"MatrixRank[{{1,2,3},{4,5,6},{7,8,9}}]==2"
"MatrixRank[{{a,b},{2*a,2*b}}]==1"
"MatrixRank[{{1,I},{I,-1}}]==1"
"Eigenvalues[ { {1,0,0}, {0,1,0}, {0,0,1}}]== {1, 1, 1}"
"DiagonalMatrix[{a,b,c}]=={{a, 0, 0}, {0, b, 0}, {0, 0, c}}"
"DiagonalMatrix[{a,b,c},1]=={{0, a, 0, 0}, {0, 0, b, 0}, {0, 0, 0, c},
{0, 0, 0, 0}}"
"DiagonalMatrix[{a,b,c},-1]=={{0, 0, 0, 0}, {a, 0, 0, 0}, {0, b, 0,
0}, {0, 0, c, 0}}"
"DiagonalMatrix[{a,b,c},2]=={{0, 0, a, 0, 0}, {0, 0, 0, b, 0}, {0, 0,
0, 0, c}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}}"
"Nest[Times,2,10]==2"
"Table[f[i], {i, 10, -5, -2}]=={f[10], f[8], f[6], f[4], f[2], f[0], f
[-2], f[-4]}"
"Dimensions[Table[100* i + 10* j + k, {i, 3}, {j, 2}, {k, 4}]]== {3,
2, 4}"
"Partition[{1,2,3,4,5,6,7,8,9,10},2]=={{1, 2}, {3, 4}, {5, 6}, {7, 8},
{9, 10}}"
"Partition[{1,2,3,4,5,6,7,8,9,10},2,1]=={{1, 2}, {2, 3}, {3, 4}, {4,
5}, {5, 6}, {6, 7}, {7, 8}, {8, 9}, {9, 10}}"
"Range[10,3]=={}"
"Range[3,10,2]== {3, 5, 7, 9}"
"Range[n,x+4]==Range[n, 4 + x]"
"Range[10,3,-1]=={10, 9, 8, 7, 6, 5, 4, 3}"
"Range[x,x+4]=={x, 1 + x, 2 + x, 3 + x, 4 + x}"
"Range[x+4,x]=={}"
"Range[x+4,x,-1]=={4 + x, 3 + x, 2 + x, 1 + x, x}"
"IntegerDigits[0]=={0}"
"Union[{a,b,c}]=={a, b, c}"
"Union[g[a,b,c],g[c,d,e]]==g[a, b, c, d, e]"
"Intersection[g[a,b,c],g[c,d,e]]==g[c]"
"Subsets[{a,b,c,d}]=={{},{a}, {a, b}, {a, b, c}, {a, b, c, d}, {a, b,
d}, {a, c}, {a, c, d}, {a, d}, {b}, {b, c}, {b, c, d}, {b, d}, {c},
{c, d}, {d}}"
"Subsets[f[a,b,c,d]]==Out[12]:= {f[],f[a], f[a, b], f[a, b, c], f[a,
b, c, d], f[a, b, d], f[a, c], f[a, c, d], f[a, d], f[b], f[b, c], f
[b, c, d], f[b, d], f[c], f[c, d], f[d]}"
"AtomQ[x]==True "
"AtomQ[123456]==True "
"AtomQ[1/10]==True "
"AtomQ[3+I]==True "
"Nest[h,x,3]==h[h[h[x]]] "
"NestList[h,x,3]=={h[x], h[h[x]], h[h[h[x]]]} "
"Fold[h,x,{a,b,c}]==h[h[h[x, a], b], c] "
"FoldList[h,x,{a,b,c}]=={x, h[x, a], h[h[x, a], b], h[h[h[x, a], b],
c]} "
"Length[{a,b,c,d}]==4"
"Length[a+b+c+d]==4"
"Length[f[g[x,y],z]]==2"
"Length[x]==0"
"Length[123456]==0"
"Length[3+I]==0"
"Length[1/10]==0"
"Length[{{a,b,c},{d,e,f}}]==2"
"Length[IntegerDigits[1000!]]==2568"
"Csc[Pi/2]==1"
"Cot[1.0]==0.64209261593433065"
"ArcCosh[2.0]==1.3169578969248166"
"Module[{x=5},x]"
"i=7"
"i++ "
"i-- "
"PermutationQ[e_List] := (Sort[e] === Range[Length[e]])"
"PermutationQ[{3,2,1}] "
"PermutationQ[{3,2,2}] "
"(p={2,3,4,5,1}
"Select[Range[20], PrimeQ[#]&]=={2, 3, 5, 7, 11, 13, 17, 19} "
"BesselJ[2,0.2]==0.004983354152783565"
"BesselY[2,0.2]==-32.15714455874636"
"BesselI[2,0.2]==0.0050166875138946783"
"BesselK[2,0.2]==49.51242928773285"
"Gamma[0.2]==4.5908437119988044"
"Plot[x^2,{x,-5,5}] "
"Plot3D[x^2+y^2,{x,-5,5},{y,-5,5}] "
"ParametricPlot[{Cos[t],Sin[t]},{t,0, 2 Pi}]"
"ListPlot[Table[{Cos[t],Sin[t]},{t,0,6.28,0.1}]]"
"ContourPlot[ Exp[-(x^2 + 3 y^2)], {x, -2, 2}, {y, -2, 2} ]"
"Erf[1.0]"
"Erfc[1.0]"
"LaplaceTransform[t,t,s]==1/s^2"
"InverseLaplaceTransform[1/s^2,s,t]==t "
"UnitStep[0.00001]"
"UnitStep[0]"
"Inverse[{{1,2},{3,4}}]=={{-2, 1}, {3/2, -1/2}}"
"Eigenvalues[{{1,2},{2,1}}]=={3, -1}"
"PartitionsP[1000]==24061467864032622473692149727991"
"LegendreQ[1,3]==1/2 (-2 +3 Log[-2])"
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