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Equation
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The Equation domain provides equations as mathematical objects.  These
are used, for example, as the input to various solve operations.

Equations are created using the equals symbol, ``=``. ::

  eq1 := 3*x + 4*y = 5 
   4y + 3x= 5
                         Type: Equation Polynomial Integer

  eq2 := 2*x + 2*y = 3 
   2y + 2x= 3
                         Type: Equation Polynomial Integer

The left- and right-hand sides of an equation are accessible using
the operations lhs and rhs. ::

  lhs eq1
   4y + 3x
                         Type: Polynomial Integer

  rhs eq1
   5
                         Type: Polynomial Integer

Arithmetic operations are supported and operate on both sides of the
equation. ::

  eq1 + eq2 
   6y + 5x= 8
                         Type: Equation Polynomial Integer

  eq1 * eq2 
     2             2
   8y  + 14x y + 6x = 15
                         Type: Equation Polynomial Integer

  2*eq2 - eq1
   x= 1
                         Type: Equation Polynomial Integer

Equations may be created for any type so the arithmetic operations
will be defined only when they make sense.  For example, exponentiation 
is not defined for equations involving non-square matrices. ::

  eq1**2
      2             2
   16y  + 24x y + 9x = 25
                          Type: Equation Polynomial Integer

Note that an equals symbol is also used to test for equality of values
in certain contexts.  For example, x+1 and y are unequal as polynomials. ::

  if x+1 = y then "equal" else "unequal"
   "unequal"
                           Type: String

  eqpol := x+1 = y 
   x + 1= y
                           Type: Equation Polynomial Integer

If an equation is used where a Boolean value is required, then
it is evaluated using the equality test from the operand type. ::

  if eqpol then "equal" else "unequal"
   "unequal"
                           Type: String

If one wants a Boolean value rather than an equation, all one has to
do is ask! ::

  eqpol::Boolean
   false
                           Type: Boolean

See Also:

* ``)show Equation``