Numerical Methods - 3.2 Linear Algebra

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
3.2.E1	${\displaystyle{\displaystyle\mathbf{A}\mathbf{x}=\mathbf{b}}}$ \mathbf{A}\mathbf{x} = \mathbf{b}		A*x = b	A*x == b	Skipped - no semantic math	Skipped - no semantic math	-	-
3.2.E5	${\displaystyle{\displaystyle\mathbf{A}=\mathbf{L}\mathbf{U}}}$ \mathbf{A} = \mathbf{L}\mathbf{U}		A = L*U	A == L*U	Skipped - no semantic math	Skipped - no semantic math	-	-
3.2.E11	${\displaystyle{\displaystyle y_{j}=f_{j}-\ell_{j}y_{j-1}}}$ y_{j} = f_{j}-\ell_{j}y_{j-1}		y[j] = f[j]- ell[j]*y[j - 1]	Subscript[y, j] == Subscript[f, j]- Subscript[\[ScriptL], j]*Subscript[y, j - 1]	Skipped - no semantic math	Skipped - no semantic math	-	-
3.2.E12	${\displaystyle{\displaystyle x_{j}=(y_{j}-u_{j}x_{j+1})/d_{j}}}$ x_{j} = (y_{j}-u_{j}x_{j+1})/d_{j}	${\displaystyle{\displaystyle j=n-1}}$	x[j] = (y[j]- u[j]*x[j + 1])/(b[j]- ell[j]*c[j - 1])	Subscript[x, j] == (Subscript[y, j]- Subscript[u, j]*Subscript[x, j + 1])/(Subscript[b, j]- Subscript[\[ScriptL], j]*Subscript[c, j - 1])	Skipped - no semantic math	Skipped - no semantic math	-	-
3.2#Ex3	${\displaystyle{\displaystyle\|\mathbf{x}\|_{p}=\left(\sum_{j=1}^{n}{\left|x_{j}\right|^{p}}\right)^{1/p}}}$ \|\mathbf{x}\|_{p} = \left(\sum_{j=1}^{n}\abs{x_{j}}^{p}\right)^{1/p}		Error	Subscript[Norm[x], p] == ((Sum[(Abs[Subscript[x, j]])^(p), {j, 1, n}, GenerateConditions->None]))^(1/p)	Failure	Failure	Error	Failed [300 / 300] Result: Plus[-1.0, Subscript[1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] Test Values: {Rule[n, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[Subscript[x, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Plus[Complex[-1.7142646344505674, 0.6191072997114272], Subscript[1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] Test Values: {Rule[n, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[Subscript[x, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
3.2.E17	${\displaystyle{\displaystyle\frac{\|\mathbf{x}^{*}-\mathbf{x}\|_{p}}{\|\mathbf{x}\|_{p}}\leq\kappa(\mathbf{A})\frac{\|\mathbf{r}\|_{p}}{\|\mathbf{b}\|_{p}}}}$ \frac{\|\mathbf{x}^{*}-\mathbf{x}\|_{p}}{\|\mathbf{x}\|_{p}} \leq \kappa(\mathbf{A})\frac{\|\mathbf{r}\|_{p}}{\|\mathbf{b}\|_{p}}		Error	Divide[Subscript[Norm[(x)^(*)- x], p],Subscript[Norm[x], p]] <= (Subscript[Norm[A], p]*Subscript[Norm[(A)^(- 1)], p])*Divide[Subscript[Norm[r], p],Subscript[Norm[b], p]]	Skipped - no semantic math	Skipped - no semantic math	-	-
3.2.E18	${\displaystyle{\displaystyle\mathbf{A}\mathbf{x}=\lambda\mathbf{x}}}$ \mathbf{A}\mathbf{x} = \lambda\mathbf{x}		A*x = lambda*x	A*x == \[Lambda]*x	Skipped - no semantic math	Skipped - no semantic math	-	-