Table of Contents
CAS-Algebra Commands
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This section will cover the Algebra commands of the HP Prime. Unless noted, the commands are practically useful only in CAS Mode and in CAS programs. RPN Entry will not be covered in this section.
Examples given in this section is with the CAS Simplify setting set to Maximum. The “Include complex results in variables” option is turned off.
simplify
Simplifies an algebraic or mathematical expression. Useful if the CAS Simplify setting is set to None or Minimum. The simplify command aims for an exact answer.
Syntax
Input:
CAS Mode Program Editor - CAS Programs
simplify(algebraic or mathematical expression)
Examples:
In Radians Mode: simplify( π/6 + ASIN(1/2) ) returns π/3
Simplifying an Algebraic Expression: simplify( x/3 - 3*x/4 + x/2 ) returns x/12
Simplify won't give approximates: simplify( Zeta(3) ) returns Zeta(3)
Access: Toolbox, CAS, 1. Algebra, 1. simplify
See Also: collect, expand, factor, subst, partfrac
collect
Collects like terms in an algebraic expression. A list of algebraic expressions can be included.
Syntax
Input:
CAS Mode Program Editor - CAS Programs
colllect(algebraic expression)
Examples:
A polynomial: collect( (x+1)²+3*x-x² ) returns 2*x²-x+1
Collecting like terms: collect( 2*a+3*b-4*a+5*b ) returns -2*a+8*b
More than one expression: collect( {5*x+3*a-x, 2*(a+x)²-a*x} ) returns [ 3*a+4*x, 2*a²+3*a*x+2*x²]
Access: Toolbox, CAS, 1. Algebra, 2. collect
See Also: simplify, expand, factor
expand
Expands an algebraic expression. Products and powers are expanded, and multiplication and division are distributed.
Syntax
Input:
CAS Mode Program Editor - CAS Programs
expand(algebraic expression)
Examples:
expand( (x+1)^3 ) returns x^3 + 3*x^2 + 3*x + 1
expand( (LN(x)-3*x)² ) returns -6*x*LN(x)+(-3*x)²+LN(x)²
Access: Toolbox, CAS, 1. Algebra, 3. expand
See Also: simplify, collect, factor
factor
Attempts to factorize an polynomial. If the polynomial cannot be factorized, the original polynomial is returned.
Syntax
Input:
CAS Mode Program Editor - CAS Programs
factor(polynomial)
Examples:
factor( x²+4*x-5 ) returns (x-1)*(x+5)
factor( x²+8*x+5 ) returns (x + -√11 + 4)*(x + √11 + 4)
factor( x²+4*x+5 ) returns x²+4*x+5
Access: Toolbox, CAS, 1. Algebra, 4. factor
See Also: simplify, collect, factor
subst
Makes a substitution a value for a variable in an algebraic expression. The substitution does not have to be a numerical constant.
Syntax
Input:
CAS Mode Program Editor - CAS Programs
subst(algebraic expression, variable = expression)
Examples:
subst( x^3 - 1, x = 4 ) returns 63
subst( x²-1,x=1/2+a ) returns (4*a²+4*a-3)/4
subst( COS(x)+3,x=ACOS(x) ) returns x+3
Access: Toolbox, CAS, 1. Algebra, 5. subst
See Also: simplify, partfrac
partfrac
Given a fraction, the partfrac performs partial fraction operation on the fraction. If the fraction is numerical, parfrac simplifies the fraction.
Syntax
Input:
CAS Mode Program Editor - CAS Programs
partfrac(algebraic expression or fraction)
Examples:
partfrac( 15/60 ) returns 1/4
partfrac( (x+2)^3/(x-2) ) returns x²+8*x+28+64/(x-2)
partfrac( (2*x+3)/(a+x) ) returns 2+(-2*x+3)/(x+a)
Access: Toolbox, CAS, 1. Algebra, 6. partfrac
See Also: simplify, subst
Extracting Commands
numer
Returns the numerator of a fraction.
Syntax
Input:
CAS Mode Program Editor - CAS Programs
numer(fraction)
Examples:
numer(8/9) returns 8
numer( x²/LN(x) ) returns x²
Access: Toolbox, CAS, 1. Algebra, 7. Extract, 1. numer
See Also: denom
denom
Returns the denominator of a fraction.
Syntax
Input:
CAS Mode Program Editor - CAS Programs
denom(fraction)
Examples:
denom(8/9) returns 9
denom( x²/LN(x) ) returns LN(x)
Access: Toolbox, CAS, 1. Algebra, 7. Extract, 2. denom
See Also: numer
left and LEFT
There are three uses:
left(equation) returns the left side of the equation.
LEFT(list or vector, number of elements) returns the leftmost elements.
LEFT(string, number of characters) returns the leftmost part of the string.
Syntax
Input:
CAS Mode Program Editor - CAS Programs
Equations: left(equation)
Lists, Vectors, or Strings: LEFT(list or vector or string, number of elements)
Home Mode
Home Mode - Textbook and Algebraic Entry Normal Program Editor
Lists and Vectors: CAS.LEFT(list of vector, number of elements)
String: LEFT(string, number of characters)
Examples: CAS Mode:
left(8+3*x = 1) returns 3*x+8
LEFT({7,8,9}, 2) returns {7, 8}
LEFT([8, 9, 2], 2) returns [8, 9]
LEFT(“abc”, 2) returns “ab”
Access: Toolbox, CAS, 1. Algebra, 7. Extract, 3. left
See Also: right
right and RIGHT
There are three uses:
right(equation) returns the right side of the equation.
RIGHT(list or vector, number of elements) returns the rightmost elements.
RIGHT(string, number of characters) returns the rightmost part of the string.
Syntax
Input:
CAS Mode Program Editor - CAS Programs
Equations: right(equation)
Lists, Vectors, or Strings: RIGHT(list or vector or string, number of elements)
Home Mode
Home Mode - Textbook and Algebraic Entry Normal Program Editor
Lists and Vectors: CAS.right(list of vector, number of elements)
String: RIGHT(string, number of characters)
Examples: CAS Mode:
right(8+3*x = 1) returns 1
RIGHT({7,8,9}, 2) returns {8, 9}
RIGHT([8, 9, 2], 2) returns [9, 2]
RIGHT(“abc”, 2) returns “bc”
Access: Toolbox, CAS, 1. Algebra, 7. Extract, 4. right
See Also: left
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