# OpenMath Content Dictionary: fieldname1

Canonical URL:
http://www.openmath.org/cd/fieldname1.ocd
CD Base:
http://www.openmath.org/cd
CD File:
fieldname1.ocd
CD as XML Encoded OpenMath:
fieldname1.omcd
Defines:
C, Q, R
Date:
2004-06-01
Version:
1 (Revision 1)
Review Date:
2006-06-01
Status:
experimental

A CD of functions for basic constructions in field theory.

Written by Arjeh M. Cohen 2004-02-25


## C

Description:

This is a symbol representing the field of complex numbers.

Commented Mathematical property (CMP):
The field of complex numbers is (C, +,0,-,*,1,/), where +,-,*,/ are the standard arithmetic operations.
Formal Mathematical property (FMP):
$C=\mathrm{field}\left(\mathbb{C},+,0,-,×,1,\frac{}{}\right)$
Signatures:
sts

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## R

Description:

This is a symbol representing the field of real numbers.

Commented Mathematical property (CMP):
The field of real numbers is (R, +,0,-,*,1,/), where +,-,*,/ are the standard arithmetic operations.
Formal Mathematical property (FMP):
$R=\mathrm{field}\left(\mathbb{R},+,0,-,×,1,\frac{}{}\right)$
Signatures:
sts

 [Next: Q] [Previous: C] [Top]

## Q

Description:

This is a symbol representing the field of rational numbers.

Commented Mathematical property (CMP):
The field of rational numbers is (Q, +,0,-,*,1,/), where +,-,*,/ are the standard arithmetic operations.
Formal Mathematical property (FMP):
$Q=\mathrm{field}\left(\mathbb{Q},+,0,-,×,1,\frac{}{}\right)$
Commented Mathematical property (CMP):
The carrier set of this field is the set of rational numbers.
Formal Mathematical property (FMP):
$\mathrm{carrier}\left(Q\right)=\mathbb{Q}$
Example:
$Q=\mathrm{field}\left(\mathbb{Q},+,0,-,×,1,\lambda x.\frac{1}{x}\right)$
Signatures:
sts

 [First: C] [Previous: R] [Top]