Note that the semicolon ``;'' in the examples above allows several expressions to be entered on one line. The result of the last expression -is displayed. remember also that the percent symbol ``%'' is used to +is displayed. Remember also that the percent symbol ``%'' is used to represent the result of a previous calculation.
@@ -912,7 +913,7 @@ is available and returns a partial fraction of one term. To decompose this further the numerator can be obtained using firstNumer and the denominator with firstDenom. The whole part of a partial fraction can be retrieved using wholePart and the number of fractional parts can -be found using the function numberOf FractionalTerms: +be found using the function numberOfFractionalTerms: diff --git a/src/axiom-website/hyperdoc/axbook/section-0.5.xhtml b/src/axiom-website/hyperdoc/axbook/section-0.5.xhtml index 06473f1..4cc26c6 100644 --- a/src/axiom-website/hyperdoc/axbook/section-0.5.xhtml +++ b/src/axiom-website/hyperdoc/axbook/section-0.5.xhtml @@ -188,9 +188,11 @@ end user for documentation purposes. -A description is placed before a calculation begins with three -``+++'' signs and a description placed after a calculation begins with -two plus symbols ``+''. The so-called ``plus plus'' comments are used +
A description is placed + before +a calculation begins with three "+" signed (i.e. "+++") +and a description placed after a calculation begins with +two plus symbols (e.g. "++"). The so-called ``plus plus'' comments are used within the algebra files and are processed by the compiler to add to the documentation. The so-called ``minus minus'' comments are ignored everywhere. diff --git a/src/axiom-website/hyperdoc/axbook/section-0.6.xhtml b/src/axiom-website/hyperdoc/axbook/section-0.6.xhtml index 3dc4e96..c8fbf2d 100644 --- a/src/axiom-website/hyperdoc/axbook/section-0.6.xhtml +++ b/src/axiom-website/hyperdoc/axbook/section-0.6.xhtml @@ -2091,9 +2091,13 @@ Type: OneDimensionalArray PositiveInteger -
(note that ARRAY1 is an abbreviation for the type -OneDimensionalArray.) Other types based on one-dimensional arrays are -Vector, String, and Bits. +
(note that +ARRAY1 is an abbreviation for the type +OneDimensionalArray.) +Other types based on one-dimensional arrays are +Vector, +String, and +Bits.
@@ -2719,11 +2723,16 @@ Type: BooleanThere are several things to point out concerning these examples. First, although flexible arrays are mutable, making copies of these arrays creates separate entities. This can be seen by the -fact that the modification of element b.2 above did not alter -a. Second, the merge! function can take an extra argument +fact that the modification of element +g.2 above did not alter +f. Second, the + merge! +function can take an extra argument before the two arrays are merged. The argument is a comparison -function and defaults to ``<='' if omitted. Lastly, - shrinkable tells the system whether or not to let flexible arrays +function and defaults to +``<='' if omitted. Lastly, + shrinkable tells the +system whether or not to let flexible arrays contract when elements are deleted from them. An explicit package reference must be given as in the example above.
diff --git a/src/axiom-website/hyperdoc/axbook/section-0.7.xhtml b/src/axiom-website/hyperdoc/axbook/section-0.7.xhtml index 84bf255..174e32b 100644 --- a/src/axiom-website/hyperdoc/axbook/section-0.7.xhtml +++ b/src/axiom-website/hyperdoc/axbook/section-0.7.xhtml @@ -1055,17 +1055,22 @@ Type: Void -It was mentioned that loops will only be left when either a break or - return statement is encountered so why can't one use the ``=>'' -operator? The reason is that the ``=>'' operator tells Axiom to leave the -current block whereas break leaves the current loop. The return -statement leave the current function. -
+It was mentioned that loops will only be left when either a + break or + return +statement is encountered so why can't one use +the ``=>'' operator? The reason is that +the ``=>'' operator tells Axiom to leave +the current block whereas +break leaves the current loop. The + return +statement leave the current function.
-To skip the rest of a loop body and continue the next iteration of the loop -use the iterate statement (the -- starts a comment in Axiom) -
+To skip the rest of a loop body and continue the next iteration of +the loop use the iterate +statement (the -- +starts a comment in Axiom)
@@ -1653,7 +1658,8 @@ Type: Void -The second form of the for loop syntax includes a `` such that'' +
The second form of the for +loop syntax includes a `` such that'' clause which must be of type Boolean:
@@ -1662,8 +1668,17 @@ clause which must be of type Boolean:for var in seg | BoolExpr repeat loopBody
-for var in list | BoolExpr repeat loopBody
+
+for
+var in
+seg |
+BoolExpr repeat
+loopBody
+for
+var in
+list |
+BoolExpr repeat
+loopBody
Axiom statements in an input file -(see Section ugInOutIn ), -can use indentation to indicate the program structure . -(see Section ugLangBlocks ). +(see Section +ugInOutIn ), +can use indentation to indicate the program structure +(see Section +ugLangBlocks ).
diff --git a/src/axiom-website/hyperdoc/axbook/section-1.4.xhtml b/src/axiom-website/hyperdoc/axbook/section-1.4.xhtml index 332e58c..cc98ee7 100644 --- a/src/axiom-website/hyperdoc/axbook/section-1.4.xhtml +++ b/src/axiom-website/hyperdoc/axbook/section-1.4.xhtml @@ -216,7 +216,8 @@ Type: Fraction Integer -To factor fractions, you have to pmap factor onto the numerator +
To factor fractions, you have to map + factor onto the numerator and denominator.
diff --git a/src/axiom-website/hyperdoc/axbook/section-1.5.xhtml b/src/axiom-website/hyperdoc/axbook/section-1.5.xhtml index 729c74e..761a65b 100644 --- a/src/axiom-website/hyperdoc/axbook/section-1.5.xhtml +++ b/src/axiom-website/hyperdoc/axbook/section-1.5.xhtml @@ -522,18 +522,25 @@ Type: FlexibleArray Integer -Flexible arrays are used to implement ``heaps.'' A heap is an -example of a data structure called a priority queue, where +
Flexible arrays are used to implement ``heaps.'' A +heap +(Heap is discussed in Section +HeapXmpPage ) +is an +example of a data structure called a +priority queue, where elements are ordered with respect to one another. A heap -(Heap is discussed in Section HeapXmpPage ) is organized so as to optimize insertion -and extraction of maximum elements. The extract! operation +is organized so as to optimize insertion +and extraction of maximum elements. The + extract! operation returns the maximum element of the heap, after destructively removing that element and reorganizing the heap so that the next maximum element is ready to be delivered.
-An easy way to create a heap is to apply the operation heap +
An easy way to create a heap is to apply the operation +heap to a list of values.
@@ -598,21 +605,28 @@ Type: List Integer -A binary tree is a ``tree'' with at most two branches -tree per node: it is either empty, or else is a node -consisting of a value, and a left and right subtree (again, binary -trees). (BinarySearchTrees are discussed in Section -BinarySearchTreeXmpPage ) -Examples of binary tree types are BinarySearchTree, -PendantTree, TournamentTree, and BalancedBinaryTree. +
A binary tree +is a ``tree'' with at most two branches +tree +per node: it is either empty, or else is a node +consisting of a value, and a left and right subtree (again, binary trees). +Examples of binary tree types are +BinarySearchTree, +PendantTree, +TournamentTree, and +BalancedBinaryTree.
A binary search tree is a binary tree such that, -tree:binary search for each node, the value of the node is -binary search tree greater than all values (if any) in the -left subtree, and less than or equal all values (if any) in the right -subtree. +tree:binary search +for each node, the value of the node is +binary search tree + greater than all values (if any) in the +left subtree, and less than or equal all values (if any) in the right subtree. +(BinarySearchTrees are discussed in Section + +BinarySearchTreeXmpPage )
@@ -643,10 +657,27 @@ Type: BinarySearchTree PositiveInteger -A balanced binary tree is useful for doing modular computations. -balanced binary tree Given a list of moduli, -tree:balanced binary modTree produces -a balanced binary tree with the values at its leaves. +
A balanced binary tree is useful for doing +modular computations. +balanced binary tree + Given a list of moduli, +tree:balanced binary + + modTree + +produces a balanced binary tree with the values + at its leaves.
@@ -691,11 +722,12 @@ corresponding structure like streams for infinite collections.+The domain constructor Quaternion +implements quaternions over commutative rings. For information on +related topics see -
The domain constructor Quaternion implements quaternions over -commutative rings. For information on related topics see -ComplexXmpPage and -OctonionXmpPage . -You can also issue the system command -)show Quaternion to display the full list of operations -defined by Quaternion. -
+ + ComplexXmpPage + and + + OctonionXmpPage +. + +You can also issue the system command +)show Quaternion +to display the full list of operations defined by +Quaternion. + -The basic operation for creating quaternions is -quaternquaternQuaternion. +
+The basic operation for creating quaternions is +quatern +quatern + +Quaternion +. This is a quaternion over the rational numbers.
- - -| - - |
| + + | +
The four arguments are the real part, the i imaginary part, the -j imaginary part, and the k imaginary part, respectively. +
+ The four arguments are the real part, the + i + imaginary part, the + j + imaginary part, and the + k + imaginary part, respectively.
- - -| - - |
| + + | +
Because q is over the rationals (and nonzero), you can invert it. +
+ Because + q + is over the rationals (and nonzero), you can invert it.
- - -| - - |
| + + | +
The usual arithmetic (ring) operations are available
- - -| - - |
| + + | +
| - - |
| + + | +
In general, multiplication is not commutative. +
+ In general, multiplication is not commutative.
- - -| - - |
| + + | +
There are no predefined constants for the imaginary i, j, -and k parts, but you can easily define them. +
+ There are no predefined constants for the imaginary + i, j, + and + k + parts, but you can easily define them.
- - -| - - |
| + + | +
These satisfy the normal identities. +
+ These satisfy the normal identities.
- - -| - - |
| + + | +
The norm is the quaternion times its conjugate. +
+ The norm is the quaternion times its conjugate.
- - -| - - |
| + + | +
| - - |
| + + | +
| - - |
| + + | +
A queue is an aggregate structure +which allows insertion at the back of the queue, deletion at the front +of the queue and inspection of the front element. Queues are similar +to a line of people where you can join the line at the back, leave the +line at the front, or see the person in the front of the line.
+ +Queues can be created from a list of elements using the +queue +Queue +function.
+ +| + + | +
+ An empty queue can be created using the + empty + function. +
+ +| + + | +
+ The + empty? + function will return + true + if the queue contains no elements. +
+ +| + + | +
+Queues modify their arguments so they use the exclamation mark "!" +as part of the function name. +
+ ++ The + dequeue! + operation removes the front element of the queue and + returns it. The queue is one element smaller. The + extract! does + the same thing with a different name. +
+ +| + + | +
| + + | +
| + + | +
+ The enqueue! + function adds a new element to the back of the + queue and returns the element that was pushed. The queue is one + element larger. The + insert! + function does the same thing with a different name. +
+ +| + + | +
| + + | +
| + + | +
+ To read the top element without changing the queue use the + front + function. +
+ +| + + | +
| + + | +
| + + | +