OpenMath Content Dictionary: linalg1p

Canonical URL:
http://www.math.kobe-u.ac.jp/OCD/linalg1p.tfb
CD File:
linalg1p.ocd
CD as XML Encoded OpenMath:
linalg1p.omcd
Defines:
kernel, minus_part, ones, plus_part
Date:
2002-07-30
Version:
1 (Revision 1)
Review Date:
2017-12-31
Status:
experimental

  Author: Nobuki Takayama

This CD defines symbols for linear algebra used for hypergeon1 (hypergeometric series of n variables).


plus_part

Description:

The argument is a vector. It replaces negative elements in the vector to zero.

Signatures:
sts


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minus_part

Description:

The argument is a vector. It replaces positive elements in the vector to zero and negative elements to their absolute values.

Commented Mathematical property (CMP):
$u = u_{+} - u_{-}$
Formal Mathematical property (FMP):
u = sub ( plus_part ( u ) , minus_part ( u ) )
Signatures:
sts


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ones

Description:

It returns a vector of a specifed size of which elements are one. 1-ary function.

Commented Mathematical property (CMP):
for all $i$, ${\vec 1}[i] = 1$
Signatures:
sts


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kernel

Description:

It returns the kernel of the map defined by a matrix in a specified domain.

Commented Mathematical property (CMP):
$\{ x \in D | A x = 0 \}$
Formal Mathematical property (FMP):
kernel ( d , a ) = { x d | a x = zero ( size ( x ) , 1 ) }
Signatures:
sts


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