Mathcad like Length redefinition

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&[DATE] &[TIME] - &[FILENAME]

This is the classic Length redefinition in mathcad for using in programs which can take scalars or matrices as arguments

Numeric evaluation

Symbolic evaluation

x Length x length 0 try 11 line :

1 Length #

1 Length 1 length

111 mat Length 1

111 mat Length 1

x Length #

x Length x length

x y z t 22 mat Length 4

x y z t 22 mat Length 4

M.01 M.10 M.00 13 mat 01 matrix 10 matrix 00 matrix 13 mat :

V u x 21 mat :

M x y z t 22 mat :

s abc :

S a b 21 sys :

Rows & Cols

Numeric

Symbolic

Rows(x) extends  rows(x) for return 0 
for atom expressions or systems. x Rows ans x rows : (0 > 0 try ans 0 if 11 line :

s Rows 1 Rows x Rows V Rows M Rows S Rows 61 sys 00022061 sys

s Rows 1 Rows x Rows V Rows M Rows S Rows 61 sys 00022061 sys

Cols(x) extends cols(x) for return 0 
for atom expressions or systems. x Cols ans x cols : (0 > 0 try ans 0 if 11 line :

M.01 Rows M.10 Rows M.00 Rows 31 sys 01031 sys

M.01 Rows M.10 Rows M.00 Rows 31 sys 01031 sys

Size(x) returns [Rows(x) Cols(x)] x Size R x rows : (C x cols : (+ 0 > 0 try R C 12 mat 0012 mat if 11 line :

s Size 1 Size x Size V Size M Size S Size 61 sys 0012 mat 0012 mat 0012 mat 2112 mat 2212 mat 0012 mat 61 sys

s Size 1 Size x Size V Size M Size S Size 61 sys 0012 mat 0012 mat 0012 mat 2112 mat 2212 mat 0012 mat 61 sys

M.01 Size M.10 Size M.00 Size 31 sys 0112 mat 1012 mat 0012 mat 31 sys

M.01 Size M.10 Size M.00 Size 31 sys 0112 mat 1012 mat 0012 mat 31 sys

IsMatrix & IsVector

IsMatrix(x) true if x is a matrix. x IsMatrix ans x rows x cols + 0 > (: 0 try ans 0 if 11 line :

s IsMatrix 1 IsMatrix x IsMatrix V IsMatrix M IsMatrix S IsMatrix 61 sys 00011061 sys

s IsMatrix 1 IsMatrix x IsMatrix V IsMatrix M IsMatrix S IsMatrix 61 sys 00011061 sys

This isn't just Rows(x)≠0 because this cases

M.01 IsMatrix M.10 IsMatrix M.00 IsMatrix 31 sys 11031 sys

M.01 IsMatrix M.10 IsMatrix M.00 IsMatrix 31 sys 11031 sys

But ...

IsVector(x) true if x is a column vector. x IsVector x Cols 1 ≡ 11 line :

s IsVector 1 IsVector x IsVector V IsVector M IsVector S IsVector 61 sys 00010061 sys

s IsVector 1 IsVector x IsVector V IsVector M IsVector S IsVector 61 sys 00010061 sys

And

M.01 IsVector M.10 IsVector M.00 IsVector 31 sys 10031 sys

M.01 IsVector M.10 IsVector M.00 IsVector 31 sys 10031 sys

If is spected more complicate structures,like

N a x y z t 22 mat * :

N IsMatrix 0

N IsMatrix 0

I use this:

IsMat(x) true if x is pressumed to be a matrix. x IsMat x num2str mat(findstr 1 - ≠ 10 if 11 line :

N IsMat 1

N IsMat 1

Notice the difference with this other

x IsMat2 x num2str mat(findstr 1 - ≠ 11 line :

N IsMat2 1

N IsMat2 311 mat 1 - ≠

IsSys(x) true if x is pressumed to be a system. x IsSys x num2str sys(findstr 1 - ≠ 10 if 11 line :

S IsSys 1

S IsSys 1

Length

Length(x) extends length(x) for 
systems and strings. x Length ans x length : (0 > 0 try ans x IsString 0 try x strlen ans x sys2mat.1 length : (0 > 0 try ans 0 if if if 11 line :

s Length 1 Length x Length V Length M Length S Length 61 sys 30024261 sys

s Length 1 Length x Length V Length M Length S Length 61 sys 30024261 sys

Get type don't give me the answer that I want

abc GetType 1 GetType x GetType 1 x 21 mat GetType x y z t 22 mat GetType a b 21 sys GetType 1221 mat GetType 1221 sys GetType 81 sys string number unknown unknown unknown unknown matrix system 81 sys

I found this in the forum, but not anotate from who (added IsDefined):

x Type x IsDefined C Clear testVar IsM# numRows testVar rows num2str : numRows 21 line : C x IsM# : c C 11 substr : c r ≡ (c, ≡ (| (c) ≡ (| c r ≡ C 61 substr s ≡ sys C 61 substr ∞ ≡ num x IsString 1 ≡ str num if if if c) ≡ str sys if if mat if 51 line unknown if 11 line :

abc Type 1 Type x Type 1 x 21 mat Type x y z t 22 mat Type a b 21 sys Type 1221 mat Type 1221 sys Type 81 sys str num unknown unknown unknown unknown mat sys 81 sys

Alvaro

M x y z t 22 mat

2 M * 2 x * 2 y * 2 z * 2 t * 22 mat

a M * a x y z t 22 mat *