Title: Theory / Unimportant / CS / Algo / Algebra and Symbolic Computation / Elementary Algorithms - Cohen
Tags: fromMath mathToDef examplesSwitchExample1 FromInstruction algoToProg computer_to_instruction hasNotNewEffectReturnsMeaning some_instruction automatedNewLineAfterCommaSpace mathToSee closed

Name: Computer algebra system
Definition: Computer program that performs symbolic mathematical operations.
Page: 2
Chapter: 1
Name2: Symbol manipulation system
Abbreviation: CAS

Name: Computer algebra language
Definition: A language used to interact with a CAS.
Page: 5
Chapter: 1
Name2: symbol programming language

Name: Mathematical pseudo-language
Page: 29
Chapter: 2
Section: 1
Abbreviation: MPL

Name: Number in arbitrary precision
Definition: Integer or fraction can have an arbitrary number of digits.
Page: 31
Chapter: 2
Section: 1

Name: A real number
Definition: A finite number of digits, includes a decimal point, and may include an optional power of 10.
Page: 31
Chapter: 2
Section: 1
Variables: In MPL,

Name: An identifier
Definition: A string of characters constructed with English letters, Greek letters, the digits 0, 1, . . . , 9, and the underscore symbol “ ”, beginning with a letter.
Page: 32
Chapter: 2
Section: 1
Variables: In MPL

Name: mathematical operators
Definition: Function forms that manipulate and analyze mathematical expressions.
Page: 33
Chapter: 2
Section: 1

Name: Undefined functions
Definition: an expression in function notation (e.g., f (x), g(x, y), h(n + 1)), whithout any attached properties.
Page: 35
Chapter: 2
Section: 1

Name: Expression evaluation
Definition: Actions taken by a CAS in response to an input expression.
Page: 35
Chapter: 2

Q: Polynomial's operator are:
-[...]
-[...]
A: Degree; Coefficient
Page: 63
Chapter: 2
Section: 3

Q: Property of sets:
-[...],
-[...].
A: Pairwise distinct elements; does not depend on the order of the elements in the set
Page: 69
Chapter: 2
Section: 4

Q: Operation on sets:
-[...],
-[...]
A: union, difference, intersection; \(x\in S\)
Page: 69
Chapter: 2
Section: 4

Name: Operation on lists
Definition: First(L), Rest(L)
Page: 72
Chapter: 2
Section: 4
Definition2: Adjoin(x,L),
Conjdef: All of
Definition3: Join \((L,M,\dots,N)\),
Definition4: Delete(L)
Definition5: Reverse (L)
Definition6: \(x\in L\)

Name: A recursive definition/algorithm
Definition: A definition/algorithm that is defined in terms of a simpler version of itself or sometimes in terms of just another version of itself.
Page: 77
Chapter: 3
Section: 1

Name: A recursive procedure
Definition: A procedure which calls itself.
Page: 80
Chapter: 3
Section: 1
Example: Evaluation of terms

Name: An atomic expression
Definition: An integer, real, symbol or reserved symbol.
Page: 81
Chapter: 3
Section: 1

Name: A compound expression
Definition: An operator with operands.
Page: 81
Chapter: 3
Section: 1

Name: The set of algebraic expressions
Definition: The least set containing:
-integers,
-symbols,
and closed under:
-sums, products, differences, quotient, factorial or function form.
Page: 84
Chapter: 3
Section: 2

Name: A parentheses level
Definition: A set of operators which are in the same set of pair of matching parentheses.
Page: 85
Chapter: 3
Section: 2
Index: 8
Kind: Def

Name: A unary postfix operator
Definition: An operator with an operand that immediatlely precedes the operator.
Page: 85
Chapter: 3
Section: 2
Example: factorial: \(n!\)

Name: A unary prefix operator
Definition: An operator with an operand that immediatlely follows the operator.
Page: 85
Chapter: 3
Section: 2
Example: negation: \(-x\)

Name: A function prefix operator
Definition: An expression in function notation with one or more operands.
Page: 85
Chapter: 3
Section: 2
Example: \(f(x,y)\)

Name: A binary infix operator
Definition: An operator with two operands, one that immediately precedes the operator and the other that immediately follows the operator.
Page: 85
Chapter: 3
Section: 2
Example: addition \(a+b\)

Name: An \(n\)-ary infix operator
Definition: An operator with \(n\) operands that are adjacent to some occurrence of the operator at the same parentheses level.
Page: 86
Chapter: 3
Section: 2
Example: addition \(a+b+\dots+z\)

Name: A complete sub-expression of \(u\)
Definition: The expression \(u\) itself
Page: 109
Chapter: 3
Section: 2
Variables: \(u\) an automatically simplified expression
Definition2: An operand of some operator in \(u\).
Conjdef: Either

Name: A mathematical algorithm
Definition: Step by step process for solving a mathematical problem that is suitable for computer implementation.
Page: 119
Chapter: 4
Section: 1

Name: Global symbol
Definition: A symbol which apears in a function/procedure that is not a formal parameter or a local variable.
Page: 137
Chapter: 4
Section: 2

Name: Local variables
Definition: A symbol which is declared inside a function/procedure which is not a parameter.
Page: 137
Chapter: 4
Section: 2

Question: Local variables is used
Answer: for programming purpose and are not placeholder for they assigned values. Must be assigned to be used, they are not unknown.
Page: 140
Chapter: 4
Section: 2

Name: Decision Structure
Definition: A way to control the flow in an algorithm.
Page: 140
Chapter: 4
Section: 2

Instruction: Free_of(u,t)
Page: prog
110
Effect: \(u\) does not contain \(t\)
Chapter: 3
Section: 2
Extra: prog

Instruction: Substitute(
  u,
  t = r
).
Page: prog
111
Effect: It forms a new expression with each occurrence of the target expression \(t\) in \(u\) replaced by the replacement expression \(r\).
Chapter: 3
Section: 2
Extra: prog

Instruction: Sequential_Substitute(
  u,
  [t_1=r_1,
  ... ,
  t_n=r_n]
).
Page: prog
114
Effect: Substitute (... Substitute (u,t_1=r_1)..., t_n=r_n)
Chapter: 3
Section: 2
Extra: prog

Instruction: Concurrent_Substitute(
  u,
  {t_1=r_1,
  ... ,
  t_n=r_n}
).
Page: prog
115
Chapter: 3
Section: 2
Returns: \(  u\) where each occurence of \(  t_i\) is replaced by \(  r_i\)
Extra: prog