11. Software calculators are provided on the Internet which are customizable to use any conceivable algebraic expression . 12. The New algebra ( 1591 ) of Fran�ois Vi�te introduced the modern notational manipulation of algebraic expressions . 13. A useful property of algebraic numbers is that equality between two algebraic expressions can be determined algorithmically. 14. Leading to the algebraic expression " QM v " for the composed output from " v " input. 15. A related class of problems is finding algebraic expressions for the roots of a polynomial in a single variable. 16. Other mathematical work includes a system he called " G�om�trographie " and a method which related algebraic expressions to geometric objects. 17. There are a lot of algebraic expressions for the golden rectangle, but it is most easily expressed as 1 to 1.618. 18. When two algebraic expressions are written next to each other, the operation of multiplication is said to be " understood ". 19. The value returned from " integrate ", although displayed as an algebraic expression , behaves differently from the same expression entered by hand. 20. There are a lot of algebraic expressions for the golden rectangle, but it is most easily expressed as 1 to 1 . 618.