FreeGroup

java.lang.Object
- org.lsmp.djep.groupJep.groups.Group
- - org.lsmp.djep.groupJep.groups.FreeGroup

All Implemented Interfaces:

GroupI, AbelianGroupI, RingI

Direct Known Subclasses:

ExtendedFreeGroup
```
public class FreeGroup
extends Group
implements RingI
```
A free group generated by a symbol t.

Constructor Summary

Constructors
Constructor and Description

FreeGroup(RingI K, String symbol)
Create the ring K(t) where t is a free variable.

Constructors
Constructor and Description
`FreeGroup(RingI K, String symbol)` Create the ring K(t) where t is a free variable.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`Number`	`add(Number a, Number b)` Get sum of the numbers
`void`	`addStandardConstants(JEP j)` adds the standard constants for this group.
`boolean`	`equals(Number a, Number b)` whether two numbers are equal
`RingI`	`getBaseRing()` Returns the base ring of this extension.
`Number`	`getInverse(Number a)` Get Inverse of a number
`Number`	`getONE()` Get multiplicative identity i.e.
`Complex`	`getRootVal()` Returns an approximation to the value of the root as a complex number.
`String`	`getSymbol()` Returns the symbol used to denote the generator.
`Number`	`getTPoly()`
`Number`	`getZERO()` Returns the identity element under +
`boolean`	`isConstantPoly(Number poly)` Whether the given polynomial is constant.
`Number`	`mul(Number a, Number b)` Returns the product of two numbers, a*b
`void`	`setRootVal(Complex complex)` Sets the value used to approximate the root as a complex number.
`boolean`	`setRootVal(String sym, Complex val)` Sets the root value for given symbol.
`Number`	`sub(Number a, Number b)` Get the difference of the numbers.
`String`	`toString()`
`Number`	`valueOf(Number[] coeffs)`
`Number`	`valueOf(String s)` returns number given by the string

Methods inherited from class org.lsmp.djep.groupJep.groups.Group
addStandardFunctions, getNumberFactory

Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface org.lsmp.djep.groupJep.GroupI
addStandardFunctions, getNumberFactory

- Constructor Detail
  - FreeGroup
```
public FreeGroup(RingI K,
                 String symbol)
```
    Create the ring K(t) where t is a free variable.
    
    Parameters:
    
    K - the Ring this is an extension of.
    
    symbol - the name of the free variable.
- Method Detail
  - add
```
public Number add(Number a,
                  Number b)
```
    Description copied from interface: GroupI
    
    Get sum of the numbers
    
    Specified by:
    
    add in interface GroupI
  - sub
```
public Number sub(Number a,
                  Number b)
```
    Description copied from interface: GroupI
    
    Get the difference of the numbers. i.e. a + (-b)
    
    Specified by:
    
    sub in interface GroupI
  - mul
```
public Number mul(Number a,
                  Number b)
```
    Description copied from interface: RingI
    
    Returns the product of two numbers, a*b
    
    Specified by:
    
    mul in interface RingI
  - equals
```
public boolean equals(Number a,
                      Number b)
```
    Description copied from interface: GroupI
    
    whether two numbers are equal
    
    Specified by:
    
    equals in interface GroupI
  - valueOf
```
public Number valueOf(String s)
```
    Description copied from interface: GroupI
    
    returns number given by the string
    
    Specified by:
    
    valueOf in interface GroupI
  - valueOf
```
public Number valueOf(Number[] coeffs)
```
  - getZERO
```
public Number getZERO()
```
    Description copied from interface: GroupI
    
    Returns the identity element under +
    
    Specified by:
    
    getZERO in interface GroupI
  - getONE
```
public Number getONE()
```
    Description copied from interface: RingI
    
    Get multiplicative identity i.e. 1. Strictly speaking a ring need not have a mul indentity. However most useful ones do, and they are not all integral domains.
    
    Specified by:
    
    getONE in interface RingI
  - getTPoly
```
public Number getTPoly()
```
  - getInverse
```
public Number getInverse(Number a)
```
    Description copied from interface: GroupI
    
    Get Inverse of a number
    
    Specified by:
    
    getInverse in interface GroupI
  - addStandardConstants
```
public void addStandardConstants(JEP j)
```
    Description copied from class: Group
    
    adds the standard constants for this group. By default does nothing.
    
    Specified by:
    
    addStandardConstants in interface GroupI
    
    Overrides:
    
    addStandardConstants in class Group
  - toString
```
public String toString()
```
    Overrides:
    
    toString in class Group
  - getBaseRing
```
public RingI getBaseRing()
```
    Returns the base ring of this extension.
  - setRootVal
```
public void setRootVal(Complex complex)
```
    Sets the value used to approximate the root as a complex number.
  - setRootVal
```
public boolean setRootVal(String sym,
                          Complex val)
```
    Sets the root value for given symbol.
    
    Parameters:
    
    sym - the symbol to set
    
    val - the complex value
    
    Returns:
    
    true is sym is a symbol for either this group or its baseRing or the basrRing's baseRing etc.
  - getRootVal
```
public Complex getRootVal()
```
    Returns an approximation to the value of the root as a complex number.
  - getSymbol
```
public String getSymbol()
```
    Returns the symbol used to denote the generator.
  - isConstantPoly
```
public boolean isConstantPoly(Number poly)
```
    Whether the given polynomial is constant.
    
    Specified by:
    
    isConstantPoly in interface GroupI
    
    Overrides:
    
    isConstantPoly in class Group

Class FreeGroup

Constructor Summary

Method Summary

Methods inherited from class org.lsmp.djep.groupJep.groups.Group

Methods inherited from class java.lang.Object

Methods inherited from interface org.lsmp.djep.groupJep.GroupI

Constructor Detail

FreeGroup

Method Detail

add

sub

mul

equals

valueOf

valueOf

getZERO

getONE

getTPoly

getInverse

addStandardConstants

toString

getBaseRing

setRootVal

setRootVal

getRootVal

getSymbol

isConstantPoly