tests/unit/matrix

printbr(Array(1,2,3))	$\left[\begin{matrix} 1 \\ 2 \\ 3\end{matrix}\right]$ GOOD	time: 0.120000ms stack: size: 0
printbr(Array(1,2) + Array(3,4))	${\left[\begin{matrix} 1 \\ 2\end{matrix}\right]} + {\left[\begin{matrix} 3 \\ 4\end{matrix}\right]}$ GOOD	time: 0.418000ms stack: size: 0
printbr((Array(1,2) + Array(3,4))())	$\left[\begin{matrix} 4 \\ 6\end{matrix}\right]$ GOOD	time: 1.630000ms stack: size: 10 Init +:Prune:combineConstants +:Prune:combineConstants +:Prune:Array.pruneAdd Prune Expand Prune Factor Prune Tidy
simplifyAssertEq((Array(1,2) + Array(3,4))(), Array(4,6))	${\left[\begin{matrix} 4 \\ 6\end{matrix}\right]} = {\left[\begin{matrix} 4 \\ 6\end{matrix}\right]}$ GOOD	time: 2.224000ms stack: size: 7 Init Prune Expand Prune Factor Prune Tidy
printbr(Matrix({1,2},{3,4}))	$\left[\begin{array}{cc} 1& 2\\ 3& 4\end{array}\right]$ GOOD	time: 0.224000ms stack: size: 0
printbr(Matrix({1,2},{3,4}):inverse())	$\left[\begin{array}{cc} -{2}& 1\\ \frac{3}{2}& -{\frac{1}{2}}\end{array}\right]$ $\left[\begin{array}{cc} 1& 0\\ 0& 1\end{array}\right]$ GOOD	time: 11.267000ms stack: size: 33 Init :Prune:apply unm:Prune:doubleNegative :Prune:apply unm:Prune:doubleNegative :Prune:apply unm:Prune:doubleNegative /:Prune:xOverMinusOne :Prune:apply unm:Prune:doubleNegative +:Prune:combineConstants ^:Prune:xToTheZero :Prune:apply /:Prune:divToPowSub :Prune:factorDenominators :Prune:apply /:Prune:xOverX :Prune:factorDenominators :Prune:matrixMul /:Prune:xOverMinusOne :Prune:apply :Prune:factorDenominators :Prune:matrixMul /:Prune:matrixScalar Prune Expand Prune Factor Prune Constant:Tidy:apply Constant:Tidy:apply /:Tidy:apply Tidy
simplifyAssertEq(Matrix({1,2},{3,4}):inverse(), Matrix({-2,1},{frac(3,2),-frac(1,2)}))	${\left[\begin{array}{cc} -{2}& 1\\ \frac{3}{2}& -{\frac{1}{2}}\end{array}\right]} = {\left[\begin{array}{cc} -2& 1\\ \frac{3}{2}& -{\frac{1}{2}}\end{array}\right]}$ GOOD	time: 14.175000ms stack: size: 12 Init :Prune:apply :Prune:factorDenominators unm:Prune:doubleNegative Prune Expand Prune Factor Prune Constant:Tidy:apply /:Tidy:apply Tidy
printbr(Matrix({a,b},{c,d}))	$\left[\begin{array}{cc} a& b\\ c& d\end{array}\right]$ GOOD	time: 0.315000ms stack: size: 0
printbr(Matrix({a,b},{c,d}):inverse())	$\left[\begin{array}{cc} \frac{d}{{{{a}} {{d}}}{-{{{b}} {{c}}}}}& -{\frac{b}{{{{a}} {{d}}}{-{{{b}} {{c}}}}}}\\ -{\frac{c}{{{{a}} {{d}}}{-{{{b}} {{c}}}}}}& \frac{a}{{{{a}} {{d}}}{-{{{b}} {{c}}}}}\end{array}\right]$ $\left[\begin{array}{cc} 1& 0\\ 0& 1\end{array}\right]$ GOOD	time: 52.494000ms stack: size: 26 Init unm:Prune:doubleNegative unm:Prune:doubleNegative unm:Prune:doubleNegative :Prune:apply :Prune:factorDenominators :Prune:factorDenominators :Prune:matrixMul :Prune:factorDenominators :Prune:apply :Prune:factorDenominators :Prune:matrixMul /:Prune:matrixScalar Prune Expand Prune +:Factor:apply /:Factor:polydiv +:Factor:apply /:Factor:polydiv +:Factor:apply /:Factor:polydiv +:Factor:apply Factor Prune Tidy
simplifyAssertEq(Matrix({a,b},{c,d}):inverse(), Matrix( {frac(d, ad-bc), frac(-b, ad-bc)}, {frac(-c, ad-bc), frac(a, ad-bc)} ))	${\left[\begin{array}{cc} \frac{d}{{{{a}} {{d}}}{-{{{b}} {{c}}}}}& -{\frac{b}{{{{a}} {{d}}}{-{{{b}} {{c}}}}}}\\ -{\frac{c}{{{{a}} {{d}}}{-{{{b}} {{c}}}}}}& \frac{a}{{{{a}} {{d}}}{-{{{b}} {{c}}}}}\end{array}\right]} = {\left[\begin{array}{cc} \frac{d}{{{{a}} {{d}}}{-{{{b}} {{c}}}}}& \frac{-{b}}{{{{a}} {{d}}}{-{{{b}} {{c}}}}}\\ \frac{-{c}}{{{{a}} {{d}}}{-{{{b}} {{c}}}}}& \frac{a}{{{{a}} {{d}}}{-{{{b}} {{c}}}}}\end{array}\right]}$ GOOD	time: 88.167000ms stack: size: 9 Init unm:Prune:doubleNegative Prune Expand Prune +:Factor:apply Factor Prune Tidy
printbr(Matrix({1,0,0,t_x},{0,1,0,t_y},{0,0,1,t_z},{0,0,0,1}))	$\left[\begin{array}{cccc} 1& 0& 0& {t_x}\\ 0& 1& 0& {t_y}\\ 0& 0& 1& {t_z}\\ 0& 0& 0& 1\end{array}\right]$ GOOD	time: 0.486000ms stack: size: 0
printbr(Matrix({1,0,0,t_x},{0,1,0,t_y},{0,0,1,t_z},{0,0,0,1}):inverse())	$\left[\begin{array}{cccc} 1& 0& 0& -{{t_x}}\\ 0& 1& 0& -{{t_y}}\\ 0& 0& 1& -{{t_z}}\\ 0& 0& 0& 1\end{array}\right]$ $\left[\begin{array}{cccc} 1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right]$ GOOD	time: 13.201000ms stack: size: 7 Init Prune Expand Prune Factor Prune Tidy
simplifyAssertEq(Matrix({1,0,0,t_x},{0,1,0,t_y},{0,0,1,t_z},{0,0,0,1}):inverse(), Matrix({1,0,0,-t_x},{0,1,0,-t_y},{0,0,1,-t_z},{0,0,0,1}))	${\left[\begin{array}{cccc} 1& 0& 0& -{{t_x}}\\ 0& 1& 0& -{{t_y}}\\ 0& 0& 1& -{{t_z}}\\ 0& 0& 0& 1\end{array}\right]} = {\left[\begin{array}{cccc} 1& 0& 0& -{{t_x}}\\ 0& 1& 0& -{{t_y}}\\ 0& 0& 1& -{{t_z}}\\ 0& 0& 0& 1\end{array}\right]}$ GOOD	time: 14.674000ms stack: size: 7 Init Prune Expand Prune Factor Prune Tidy
printbr(m + mInv)	${\left[\begin{array}{cc} \cos\left( \theta\right)& -{\sin\left( \theta\right)}\\ \sin\left( \theta\right)& \cos\left( \theta\right)\end{array}\right]} + {\left[\begin{array}{cc} \cos\left( \theta\right)& \sin\left( \theta\right)\\ -{\sin\left( \theta\right)}& \cos\left( \theta\right)\end{array}\right]}$ GOOD	time: 2.174000ms stack: size: 0
printbr((m + mInv)())	$\left[\begin{array}{cc} {{2}} {{\cos\left( \theta\right)}}& 0\\ 0& {{2}} {{\cos\left( \theta\right)}}\end{array}\right]$ GOOD	time: 7.618000ms stack: size: 18 Init unm:Prune:doubleNegative unm:Prune:doubleNegative +:Prune:flattenAddMul :Prune:apply +:Prune:flattenAddMul +:Prune:Array.pruneAdd :Prune:apply +:Prune:flattenAddMul +:Prune:flattenAddMul +:Prune:Array.pruneAdd +:Prune:Array.pruneAdd Prune Expand Prune Factor Prune Tidy
printbr(m * mInv)	${{\left[\begin{array}{cc} \cos\left( \theta\right)& -{\sin\left( \theta\right)}\\ \sin\left( \theta\right)& \cos\left( \theta\right)\end{array}\right]}} {{\left[\begin{array}{cc} \cos\left( \theta\right)& \sin\left( \theta\right)\\ -{\sin\left( \theta\right)}& \cos\left( \theta\right)\end{array}\right]}}$ GOOD	time: 0.470000ms stack: size: 0
printbr((m * mInv)())	$\left[\begin{array}{cc} {{\cos\left( \theta\right)}^{2}} + {{\sin\left( \theta\right)}^{2}}& 0\\ 0& {{\cos\left( \theta\right)}^{2}} + {{\sin\left( \theta\right)}^{2}}\end{array}\right]$ GOOD	time: 10.489000ms stack: size: 34 Init unm:Prune:doubleNegative unm:Prune:doubleNegative +:Prune:combineConstants :Prune:combinePows +:Prune:combineConstants :Prune:combinePows :Prune:apply +:Prune:combineMultipliedConstants :Prune:apply +:Prune:combineMultipliedConstants +:Prune:combineConstants :Prune:combinePows +:Prune:combineConstants :Prune:combinePows :Prune:matrixMul Prune ^:Expand:integerPower ^:Expand:integerPower ^:Expand:integerPower ^:Expand:integerPower Expand +:Prune:combineConstants :Prune:combinePows +:Prune:combineConstants :Prune:combinePows +:Prune:combineConstants :Prune:combinePows +:Prune:combineConstants *:Prune:combinePows Prune Factor Prune Tidy
simplifyAssertEq( (m*mInv)(), Matrix({1,0},{0,1}) )	${\left[\begin{array}{cc} {{\cos\left( \theta\right)}^{2}} + {{\sin\left( \theta\right)}^{2}}& 0\\ 0& {{\cos\left( \theta\right)}^{2}} + {{\sin\left( \theta\right)}^{2}}\end{array}\right]} = {\left[\begin{array}{cc} 1& 0\\ 0& 1\end{array}\right]}$ GOOD	time: 16.686000ms stack: size: 7 Init Prune Expand Prune Factor Prune Tidy
printbr(m*m)	${{\left[\begin{array}{cc} \cos\left( \theta\right)& -{\sin\left( \theta\right)}\\ \sin\left( \theta\right)& \cos\left( \theta\right)\end{array}\right]}} {{\left[\begin{array}{cc} \cos\left( \theta\right)& -{\sin\left( \theta\right)}\\ \sin\left( \theta\right)& \cos\left( \theta\right)\end{array}\right]}}$ GOOD	time: 0.672000ms stack: size: 0
printbr((m*m)())	$\left[\begin{array}{cc} {{\left({{\cos\left( \theta\right)} + {\sin\left( \theta\right)}}\right)}} {{\left({{\cos\left( \theta\right)}{-{\sin\left( \theta\right)}}}\right)}}& -{{{2}} {{\cos\left( \theta\right)}} {{\sin\left( \theta\right)}}}\\ {{2}} {{\cos\left( \theta\right)}} {{\sin\left( \theta\right)}}& {{\left({{\cos\left( \theta\right)} + {\sin\left( \theta\right)}}\right)}} {{\left({{\cos\left( \theta\right)}{-{\sin\left( \theta\right)}}}\right)}}\end{array}\right]$ GOOD	time: 32.874000ms stack: size: 52 Init unm:Prune:doubleNegative unm:Prune:doubleNegative +:Prune:combineConstants :Prune:combinePows +:Prune:combineConstants :Prune:combinePows +:Prune:combineMultipliedConstants +:Prune:combineMultipliedConstants +:Prune:combineConstants :Prune:combinePows +:Prune:combineConstants :Prune:combinePows :Prune:matrixMul Prune ^:Expand:integerPower ^:Expand:integerPower ^:Expand:integerPower ^:Expand:integerPower Expand +:Prune:combineConstants :Prune:combinePows +:Prune:combineConstants :Prune:combinePows +:Prune:combineConstants :Prune:combinePows +:Prune:combineConstants *:Prune:combinePows Prune /:Prune:xOverX ^:Prune:xToTheOne /:Prune:xOverX ^:Prune:xToTheOne /:Prune:xOverX ^:Prune:xToTheOne /:Prune:xOverX ^:Prune:xToTheOne unm:Prune:doubleNegative +:Factor:apply +:Factor:apply +:Factor:apply Factor Prune Expand Prune Factor Prune Expand Prune Factor Prune Tidy
printbr(m1)	$\left[\begin{array}{cc} 1& a\\ 0& 1\end{array}\right]$ GOOD	time: 0.109000ms stack: size: 0
printbr(m2)	$\left[\begin{array}{cc} 1& 0\\ b& 1\end{array}\right]$ GOOD	time: 0.085000ms stack: size: 0
printbr((m1m2):eq((m1m2)()))	${{{\left[\begin{array}{cc} 1& a\\ 0& 1\end{array}\right]}} {{\left[\begin{array}{cc} 1& 0\\ b& 1\end{array}\right]}}} = {\left[\begin{array}{cc} {1} + {{{a}} {{b}}}& a\\ b& 1\end{array}\right]}$ GOOD	time: 2.505000ms stack: size: 13 Init +:Prune:combineConstants +:Prune:combineConstants :Prune:apply +:Prune:combineConstants :Prune:matrixMul Prune Expand Prune +:Factor:apply Factor Prune Tidy
printbr((m2m1):eq((m2m1)()))	${{{\left[\begin{array}{cc} 1& 0\\ b& 1\end{array}\right]}} {{\left[\begin{array}{cc} 1& a\\ 0& 1\end{array}\right]}}} = {\left[\begin{array}{cc} 1& a\\ b& {1} + {{{a}} {{b}}}\end{array}\right]}$ GOOD	time: 2.171000ms stack: size: 14 Init :Prune:apply +:Prune:combineConstants +:Prune:combineConstants +:Prune:combineConstants +:Prune:combineConstants :Prune:matrixMul Prune Expand Prune +:Factor:apply Factor Prune Tidy
printbr(m1:eq(m2))	${\left[\begin{array}{cc} 1& a\\ 0& 1\end{array}\right]} = {\left[\begin{array}{cc} 1& 0\\ b& 1\end{array}\right]}$ GOOD	time: 0.108000ms stack: size: 0
simplifyAssertNe(m1, m2)	${\left[\begin{array}{cc} 1& a\\ 0& 1\end{array}\right]} \ne {\left[\begin{array}{cc} 1& 0\\ b& 1\end{array}\right]}$ GOOD	time: 0.569000ms stack: size: 7 Init Prune Expand Prune Factor Prune Tidy
printbr((m1m2):eq(m2m1))	${{{\left[\begin{array}{cc} 1& a\\ 0& 1\end{array}\right]}} {{\left[\begin{array}{cc} 1& 0\\ b& 1\end{array}\right]}}} = {{{\left[\begin{array}{cc} 1& 0\\ b& 1\end{array}\right]}} {{\left[\begin{array}{cc} 1& a\\ 0& 1\end{array}\right]}}}$ GOOD	time: 0.810000ms stack: size: 0
simplifyAssertNe(m1m2, m2m1)	${{{\left[\begin{array}{cc} 1& a\\ 0& 1\end{array}\right]}} {{\left[\begin{array}{cc} 1& 0\\ b& 1\end{array}\right]}}} \ne {{{\left[\begin{array}{cc} 1& 0\\ b& 1\end{array}\right]}} {{\left[\begin{array}{cc} 1& a\\ 0& 1\end{array}\right]}}}$ GOOD	time: 5.702000ms stack: size: 14 Init :Prune:apply +:Prune:combineConstants +:Prune:combineConstants +:Prune:combineConstants +:Prune:combineConstants :Prune:matrixMul Prune Expand Prune +:Factor:apply Factor Prune Tidy
printbr((m1m2):eq(m1m2))	${{{\left[\begin{array}{cc} 1& a\\ 0& 1\end{array}\right]}} {{\left[\begin{array}{cc} 1& 0\\ b& 1\end{array}\right]}}} = {{{\left[\begin{array}{cc} 1& a\\ 0& 1\end{array}\right]}} {{\left[\begin{array}{cc} 1& 0\\ b& 1\end{array}\right]}}}$ GOOD	time: 0.568000ms stack: size: 0
simplifyAssertEq(m1m2, m1m2)	${{{\left[\begin{array}{cc} 1& a\\ 0& 1\end{array}\right]}} {{\left[\begin{array}{cc} 1& 0\\ b& 1\end{array}\right]}}} = {{{\left[\begin{array}{cc} 1& a\\ 0& 1\end{array}\right]}} {{\left[\begin{array}{cc} 1& 0\\ b& 1\end{array}\right]}}}$ GOOD	time: 4.758000ms stack: size: 13 Init +:Prune:combineConstants +:Prune:combineConstants :Prune:apply +:Prune:combineConstants :Prune:matrixMul Prune Expand Prune +:Factor:apply Factor Prune Tidy
printbr((m1m2):eq(m2m1)())	${\left[\begin{array}{cc} {1} + {{{a}} {{b}}}& a\\ b& 1\end{array}\right]} = {\left[\begin{array}{cc} 1& a\\ b& {1} + {{{a}} {{b}}}\end{array}\right]}$ GOOD	time: 4.158000ms stack: size: 14 Init :Prune:apply +:Prune:combineConstants +:Prune:combineConstants +:Prune:combineConstants +:Prune:combineConstants :Prune:matrixMul Prune Expand Prune +:Factor:apply Factor Prune Tidy
simplifyAssertNe((m1m2)(), (m2m1)())	${\left[\begin{array}{cc} {1} + {{{a}} {{b}}}& a\\ b& 1\end{array}\right]} \ne {\left[\begin{array}{cc} 1& a\\ b& {1} + {{{a}} {{b}}}\end{array}\right]}$ GOOD	time: 7.784000ms stack: size: 8 Init Prune Expand Prune +:Factor:apply Factor Prune Tidy
printbr((Matrix({a},{b}) + Matrix({c},{d})) / t)	${\frac{1}{t}}{\left({{\left[\begin{array}{c} a\\ b\end{array}\right]} + {\left[\begin{array}{c} c\\ d\end{array}\right]}}\right)}$ GOOD	time: 0.369000ms stack: size: 0
printbr(((Matrix({a},{b}) + Matrix({c},{d})) / t)())	$\left[\begin{array}{c} {\frac{1}{t}}{\left({{a} + {c}}\right)}\\ {\frac{1}{t}}{\left({{b} + {d}}\right)}\end{array}\right]$ GOOD	time: 12.985000ms stack: size: 33 Init +:Prune:Array.pruneAdd +:Prune:Array.pruneAdd +:Prune:Array.pruneAdd :Prune:apply :Prune:factorDenominators :Prune:matrixMul :Prune:apply :Prune:factorDenominators :Prune:matrixMul /:Prune:matrixScalar Prune Expand Prune +:Factor:apply /:Factor:polydiv +:Factor:apply /:Factor:polydiv Factor unm:Prune:doubleNegative +:Prune:combineConstants ^:Prune:xToTheZero :Prune:apply /:Prune:divToPowSub :Prune:factorDenominators unm:Prune:doubleNegative +:Prune:combineConstants ^:Prune:xToTheZero :Prune:apply /:Prune:divToPowSub :Prune:factorDenominators Prune Tidy
simplifyAssertEq( ((Matrix({a},{b}) + Matrix({c},{d})) / t)(), Matrix({frac(a+c,t)}, {frac(b+d,t)}) )	${\left[\begin{array}{c} {\frac{1}{t}}{\left({{a} + {c}}\right)}\\ {\frac{1}{t}}{\left({{b} + {d}}\right)}\end{array}\right]} = {\left[\begin{array}{c} {\frac{1}{t}}{\left({{a} + {c}}\right)}\\ {\frac{1}{t}}{\left({{b} + {d}}\right)}\end{array}\right]}$ GOOD	time: 14.274000ms stack: size: 15 Init Prune Expand Prune +:Factor:apply /:Factor:polydiv Factor unm:Prune:doubleNegative +:Prune:combineConstants ^:Prune:xToTheZero :Prune:apply /:Prune:divToPowSub :Prune:factorDenominators Prune Tidy
printbr(Matrix({1,2},{3,4}):inverse(Matrix({5},{6})))	$\left[\begin{array}{c} -{4}\\ \frac{9}{2}\end{array}\right]$ $\left[\begin{array}{cc} 1& 0\\ 0& 1\end{array}\right]$ GOOD	time: 7.842000ms stack: size: 7 Init Prune Expand Prune Factor Prune Tidy
printbr((Matrix({1,2},{3,4})*Matrix({1,2},{3,4}):inverse(Matrix({5},{6})))())	$\left[\begin{array}{c} 5\\ 6\end{array}\right]$ GOOD	time: 6.820000ms stack: size: 27 Init :Prune:apply unm:Prune:doubleNegative :Prune:apply unm:Prune:doubleNegative +:Prune:combineConstants ^:Prune:xToTheZero :Prune:apply /:Prune:divToPowSub :Prune:factorDenominators +:Prune:combineConstants :Prune:apply :Prune:apply unm:Prune:doubleNegative +:Prune:combineConstants ^:Prune:xToTheZero :Prune:apply /:Prune:divToPowSub :Prune:factorDenominators +:Prune:combineConstants *:Prune:matrixMul Prune Expand Prune Factor Prune Tidy
simplifyAssertEq( (Matrix({1,2},{3,4})*Matrix({1,2},{3,4}):inverse(Matrix({5},{6})))(), Matrix({5},{6}) )	${\left[\begin{array}{c} 5\\ 6\end{array}\right]} = {\left[\begin{array}{c} 5\\ 6\end{array}\right]}$ GOOD	time: 9.603000ms stack: size: 7 Init Prune Expand Prune Factor Prune Tidy