printbr(Array(1,2,3))
|
$\left[\begin{matrix} 1 \\ 2 \\ 3\end{matrix}\right]$
GOOD |
time: 0.215000ms 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: 0.735000ms stack: size: 0 |
printbr((Array(1,2) + Array(3,4))())
|
$\left[\begin{matrix} 4 \\ 6\end{matrix}\right]$
GOOD |
time: 3.575000ms stack: size: 10
|
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: 4.156000ms stack: size: 7
|
printbr(Matrix({1,2},{3,4}))
|
$\left[\begin{array}{cc} 1& 2\\ 3& 4\end{array}\right]$
GOOD |
time: 0.520000ms 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: 15.790000ms stack: size: 33
|
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: 21.343000ms stack: size: 12
|
printbr(Matrix({a,b},{c,d}))
|
$\left[\begin{array}{cc} a& b\\ c& d\end{array}\right]$
GOOD |
time: 0.530000ms 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: 106.323000ms stack: size: 20
|
simplifyAssertEq(Matrix({a,b},{c,d}):inverse(), Matrix( {frac(d, a*d-b*c), frac(-b, a*d-b*c)}, {frac(-c, a*d-b*c), frac(a, a*d-b*c)} ))
|
${\left[\begin{array}{cc} \frac{d}{{{{a}} {{d}}}{-{{{b}} {{c}}}}}& -{\frac{b}{{{{a}} {{d}}}{-{{{b}} {{c}}}}}}\\ -{\frac{c}{{{{a}} {{d}}}{-{{{b}} {{c}}}}}}& \frac{a}{{{{a}} {{d}}}{-{{{b}} {{c}}}}}\end{array}\right]} = {\left[\begin{array}{cc} \frac{d}{{{{a}} {{d}}}{-{{{b}} {{c}}}}}& \frac{-{b}}{{{{a}} {{d}}}{-{{{b}} {{c}}}}}\\ \frac{-{c}}{{{{a}} {{d}}}{-{{{b}} {{c}}}}}& \frac{a}{{{{a}} {{d}}}{-{{{b}} {{c}}}}}\end{array}\right]}$
GOOD |
time: 173.512000ms stack: size: 9
|
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: 1.043000ms 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: 24.833000ms stack: size: 7
|
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: 30.313000ms stack: size: 7
|
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: 2.304000ms 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: 10.911000ms stack: size: 20
|
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: 2.043000ms 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: 10.678000ms stack: size: 34
|
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: 20.799000ms stack: size: 7
|
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: 1.164000ms 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: 50.064000ms stack: size: 52
|
printbr(m1)
|
$\left[\begin{array}{cc} 1& a\\ 0& 1\end{array}\right]$
GOOD |
time: 0.339000ms stack: size: 0 |
printbr(m2)
|
$\left[\begin{array}{cc} 1& 0\\ b& 1\end{array}\right]$
GOOD |
time: 0.124000ms stack: size: 0 |
printbr((m1*m2):eq((m1*m2)()))
|
${{{\left[\begin{array}{cc} 1& a\\ 0& 1\end{array}\right]}} {{\left[\begin{array}{cc} 1& 0\\ b& 1\end{array}\right]}}} = {\left[\begin{array}{cc} {1} + {{{a}} {{b}}}& a\\ b& 1\end{array}\right]}$
GOOD |
time: 4.882000ms stack: size: 12
|
printbr((m2*m1):eq((m2*m1)()))
|
${{{\left[\begin{array}{cc} 1& 0\\ b& 1\end{array}\right]}} {{\left[\begin{array}{cc} 1& a\\ 0& 1\end{array}\right]}}} = {\left[\begin{array}{cc} 1& a\\ b& {1} + {{{a}} {{b}}}\end{array}\right]}$
GOOD |
time: 5.313000ms stack: size: 13
|
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: 0.194000ms 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: 1.278000ms stack: size: 7
|
printbr((m1*m2):eq(m2*m1))
|
${{{\left[\begin{array}{cc} 1& a\\ 0& 1\end{array}\right]}} {{\left[\begin{array}{cc} 1& 0\\ b& 1\end{array}\right]}}} = {{{\left[\begin{array}{cc} 1& 0\\ b& 1\end{array}\right]}} {{\left[\begin{array}{cc} 1& a\\ 0& 1\end{array}\right]}}}$
GOOD |
time: 1.448000ms stack: size: 0 |
simplifyAssertNe(m1*m2, m2*m1)
|
${{{\left[\begin{array}{cc} 1& a\\ 0& 1\end{array}\right]}} {{\left[\begin{array}{cc} 1& 0\\ b& 1\end{array}\right]}}} \ne {{{\left[\begin{array}{cc} 1& 0\\ b& 1\end{array}\right]}} {{\left[\begin{array}{cc} 1& a\\ 0& 1\end{array}\right]}}}$
GOOD |
time: 7.136000ms stack: size: 13
|
printbr((m1*m2):eq(m1*m2))
|
${{{\left[\begin{array}{cc} 1& a\\ 0& 1\end{array}\right]}} {{\left[\begin{array}{cc} 1& 0\\ b& 1\end{array}\right]}}} = {{{\left[\begin{array}{cc} 1& a\\ 0& 1\end{array}\right]}} {{\left[\begin{array}{cc} 1& 0\\ b& 1\end{array}\right]}}}$
GOOD |
time: 0.519000ms stack: size: 0 |
simplifyAssertEq(m1*m2, m1*m2)
|
${{{\left[\begin{array}{cc} 1& a\\ 0& 1\end{array}\right]}} {{\left[\begin{array}{cc} 1& 0\\ b& 1\end{array}\right]}}} = {{{\left[\begin{array}{cc} 1& a\\ 0& 1\end{array}\right]}} {{\left[\begin{array}{cc} 1& 0\\ b& 1\end{array}\right]}}}$
GOOD |
time: 10.008000ms stack: size: 12
|
printbr((m1*m2):eq(m2*m1)())
|
${\left[\begin{array}{cc} {1} + {{{a}} {{b}}}& a\\ b& 1\end{array}\right]} = {\left[\begin{array}{cc} 1& a\\ b& {1} + {{{a}} {{b}}}\end{array}\right]}$
GOOD |
time: 9.029000ms stack: size: 13
|
simplifyAssertNe((m1*m2)(), (m2*m1)())
|
${\left[\begin{array}{cc} {1} + {{{a}} {{b}}}& a\\ b& 1\end{array}\right]} \ne {\left[\begin{array}{cc} 1& a\\ b& {1} + {{{a}} {{b}}}\end{array}\right]}$
GOOD |
time: 13.657000ms stack: size: 9
|
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: 0.920000ms 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: 19.850000ms stack: size: 33
|
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: 20.398000ms stack: size: 15
|
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: 8.832000ms stack: size: 7
|
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: 13.951000ms stack: size: 27
|
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: 10.058000ms stack: size: 7
|