OpenMath Content Dictionary: veccalc1

Canonical URL:
http://www.openmath.org/cd/veccalc1.ocd
CD File:
veccalc1.ocd
CD as XML Encoded OpenMath:
veccalc1.omcd
Defines:
curl, divergence, grad, Laplacian
Date:
2001-03-12
Version:
2
Review Date:
2003-04-01
Status:
official
Uses CD:
arith1, list1, linalg1, linalg2, calculus1, relation1

This CD contains symbols to represent functions which are concerned with vector calculus.


divergence

This symbol is used to represent the divergence function. It takes one argument which should be a vector of scalar valued functions, intended to represent a vector valued function and returns a scalar value. It should satisfy the defining relation: divergence(F) = \partial(F_(x_1))/\partial(x_1) + ... + \partial(F_(x_n))/\partial(x_n)

Commented Mathematical property (CMP):
divergence(F) = \partial(F_(x_1))/\partial(x_1) + ... + \partial(F_(x_n))/\partial(x_n)
Signatures:
sts


[Next: grad] [Last: Laplacian] [Top]

grad

This symbol is used to represent the grad function. It takes one argument which should be a scalar valued function and returns a vector of functions. It should satisfy the defining relation: grad(F) = (\partial(F)/\partial(x_1), ... ,\partial(F)/partial(x_n))

Commented Mathematical property (CMP):
grad(F) = (\partial(F)/\partial(x_1), ... ,\partial(F)/partial(x_n))
Signatures:
sts


[Next: curl] [Previous: divergence] [Top]

curl

This symbol is used to represent the curl function. It takes one argument which should be a vector of scalar valued functions, intended to represent a vector valued function and returns a vector of functions. It should satisfy the defining relation: curl(F) = i X \partial(F)/\partial(x) + j X \partial(F)/\partial(y) + j X \partial(F)/\partial(Z) where i,j,k are the unit vectors corresponding to the x,y,z axes respectively and the multiplication X is cross multiplication.

Commented Mathematical property (CMP):
curl(F) = i X \partial(F)/\partial(x) + j X \partial(F)/\partial(y) + j X \partial(F)/\partial(Z)
Formal Mathematical property (FMP):
<OMOBJ>
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMA>
      <OMS cd="veccalc1" name="curl"/>
      <OMV name="F"/>
    </OMA>
    <OMA>
      <OMS cd="arith1" name="plus"/>
      <OMA>
        <OMS cd="linalg1" name="vectorproduct"/>
	<OMA>
	  <OMS cd="linalg2" name="vector"/>
	  <OMI> 1 </OMI>
	  <OMI> 0 </OMI>
	  <OMI> 0 </OMI>
	</OMA>
	<OMA>
	  <OMS cd="calculus1" name="partialdiff"/>
	  <OMA>
	    <OMS cd="list1" name="list"/>
	    <OMI> 1 </OMI>
	  </OMA>
	  <OMV name="F"/>
	</OMA>
      </OMA>
      <OMA>
        <OMS cd="linalg1" name="vectorproduct"/>
	<OMA>
	  <OMS cd="linalg2" name="vector"/>
	  <OMI> 0 </OMI>
	  <OMI> 1 </OMI>
	  <OMI> 0 </OMI>
	</OMA>
	<OMA>
	  <OMS cd="calculus1" name="partialdiff"/>
	  <OMA>
	    <OMS cd="list1" name="list"/>
	    <OMI> 2 </OMI>
	  </OMA>
	  <OMV name="F"/>
	</OMA>
      </OMA>
      <OMA>
        <OMS cd="linalg1" name="vectorproduct"/>
	<OMA>
	  <OMS cd="linalg2" name="vector"/>
	  <OMI> 0 </OMI>
	  <OMI> 0 </OMI>
	  <OMI> 1 </OMI>
	</OMA>
	<OMA>
	  <OMS cd="calculus1" name="partialdiff"/>
	  <OMA>
	    <OMS cd="list1" name="list"/>
	    <OMI> 3 </OMI>
	  </OMA>
	  <OMV name="F"/>
	</OMA>
      </OMA>
    </OMA>
  </OMA>
</OMOBJ>

eq (curl ( F) , plus (vectorproduct (vector ( 1 , 0 , 0 ) , partialdiff (list ( 1 ) , F) ) , vectorproduct (vector ( 0 , 1 , 0 ) , partialdiff (list ( 2 ) , F) ) , vectorproduct (vector ( 0 , 0 , 1 ) , partialdiff (list ( 3 ) , F) ) ) )

Signatures:
sts


[Next: Laplacian] [Previous: grad] [Top]

Laplacian

This symbol is used to represent the laplacian function. It takes one argument which should be a vector of scalar valued functions, intended to represent a vector valued function and returns a vector of functions. It should satisfy the defining relation: laplacian(F) = \partial^2(F)/\partial(x_1)^2 + ... + \partial^2(F)/\partial(x_n)^2

Commented Mathematical property (CMP):
laplacian(F) = \partial^2(F)/\partial(x_1)^2 + ... + \partial^2(F)/\partial(x_n)^2
Signatures:
sts


[First: divergence] [Previous: curl] [Top]