9.19 Equation

The Equation domain provides equations as mathematical objects. These are used, for example, as the input to various solvesolveTransSolvePackage 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 lhslhsEquation and rhsrhsEquation.

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

\[\]

8y2+14xy+6x2=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

\[\]

16y2+24xy+9x2=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}