OpenMath Content Dictionary: poly1p

Canonical URL:
http://www.math.kobe-u.ac.jp/OCD/poly1p.tfb
CD File:
poly1p.ocd
CD as XML Encoded OpenMath:
poly1p.omcd
Defines:
index, indexed_variable, multi_power, sorted_set_of_indexed_variables, vector_of_indexed_variables
Date:
2002-08-08
Version:
1 (Revision 2)
Review Date:
2017-12-31
Status:
experimental

  Author: Nobuki Takayama

This CD defines symbols for concerning multi-index and indexed variables.


multi_power

Description:

multi_power is for using the multi-index notation.

Commented Mathematical property (CMP):
$\prod_{i=1}^n x_i ^ {e_i}$
Formal Mathematical property (FMP):
multi_power ( x , e ) = i = 1 size ( x ) x i e i
Signatures:
sts


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index

Description:

index returns the index of a given indexed variable.

Signatures:
sts


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indexed_variable

Description:

indexed_variable(x,i) returns the variable x_i

Commented Mathematical property (CMP):
index(indexed_variable(x,i)) = i
Formal Mathematical property (FMP):
index ( indexed_variable ( x , i ) ) = i
Commented Mathematical property (CMP):
index(indexed_variable(x,[1,2])) = [1,2]
Formal Mathematical property (FMP):
index ( indexed_variable ( x , ( 1 , 2 ) ) ) = ( 1 , 2 )
Signatures:
sts


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vector_of_indexed_variables

Description:

vector_of_indexed_variables(x,n) returns the vector of variables (x_1, ..., x_n). vector_of_indexed_variables(x,[m,n]) returns the vector of variables (x_{1,1}, ..., x_{m,n}). Any vector of numbers can be given as an argument.

Commented Mathematical property (CMP):
i-th element of vector_of_indexed_variable(x,n) is indexed_variable(x,i)
Formal Mathematical property (FMP):
vector_of_indexed_variables ( x , n ) i = indexed_variable ( x , i )
Signatures:
sts


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sorted_set_of_indexed_variables

Description:

sorted_set_of_indexed_variables(x,s) returns the vector of variables indexed by the sorted set s.

Commented Mathematical property (CMP):
m-element of sorted_set_of_indexed_variables(x,s) is indexed_variable(x,m)
Formal Mathematical property (FMP):
index_set_selector ( m , sorted_set_of_indexed_variables ( x , s ) ) = indexed_variable ( x , m )
Signatures:
sts


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