Definition

1. Adverb:
   • In a manner relating to or using algebra: Pertaining to the branch of mathematics concerning symbols and the rules for manipulating them, or performed using algebraic methods.
   • In terms of algebra: Expressed or solved by means of algebraic equations, operations, or reasoning.

Usage Examples

• Adverb:
  • The equation was solved algebraically, without using a graph.
  • We can prove this theorem algebraically.
  • The relationship between the variables is best understood algebraically.

Advanced Usage

• "algebraically closed field": In advanced mathematics, a field is algebraically closed if every non-constant polynomial has a root within that field.
  • The field of complex numbers is algebraically closed.
• "algebraically independent": A set of numbers is algebraically independent if no non-zero polynomial equation with integer coefficients exists that relates them.
  • The numbers π and e are conjectured to be algebraically independent.

Variants and Related Words

• Algebraic (adj): Of, relating to, or using algebra.
  • An algebraic expression.
• Algebra (n): The branch of mathematics dealing with symbols and the rules for manipulating those symbols.
  • She is studying linear algebra.

Synonyms

• By algebraic methods: Using the techniques of algebra.
• Symbolically: Represented by symbols, often in a mathematical context (this is a close conceptual synonym in many mathematical contexts).

Related Phrases

• To manipulate algebraically: To transform or solve an expression using algebraic rules.
  • You must manipulate the terms algebraically to isolate the variable.
• To express algebraically: To write something using algebraic notation.
  • The rule can be expressed algebraically as y = mx + c.

Adverb

1. in an algebraic manner
   • algebraically determined