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| <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> | ||
| <html><head><title>Python: module mpyc.bfield</title> | ||
| <meta http-equiv="Content-Type" content="text/html; charset=utf-8"> | ||
| </head><body bgcolor="#f0f0f8"> | ||
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| <table width="100%" cellspacing=0 cellpadding=2 border=0 summary="heading"> | ||
| <tr bgcolor="#7799ee"> | ||
| <td valign=bottom> <br> | ||
| <font color="#ffffff" face="helvetica, arial"> <br><big><big><strong><a href="mpyc.html"><font color="#ffffff">mpyc</font></a>.bfield</strong></big></big></font></td | ||
| ><td align=right valign=bottom | ||
| ><font color="#ffffff" face="helvetica, arial"><a href=".">index</a><br><a href="file:c%3A%5Cusers%5Cberry%5Cdocuments%5Cgithub%5Cmympyc%5Cmpyc%5Cbfield.py">c:\users\berry\documents\github\mympyc\mpyc\bfield.py</a></font></td></tr></table> | ||
| <p><tt>This module supports Galois (finite) fields of characteristic 2.<br> | ||
| <br> | ||
| Function GF creates types implementing binary fields.<br> | ||
| Instantiate an <a href="builtins.html#object">object</a> from a field and subsequently apply overloaded<br> | ||
| operators such as + (addition), - (subtraction), * (multiplication),<br> | ||
| and / (division), etc., to compute with field elements.<br> | ||
| In-place versions of the field operators are also provided.</tt></p> | ||
| <p> | ||
| <table width="100%" cellspacing=0 cellpadding=2 border=0 summary="section"> | ||
| <tr bgcolor="#aa55cc"> | ||
| <td colspan=3 valign=bottom> <br> | ||
| <font color="#ffffff" face="helvetica, arial"><big><strong>Modules</strong></big></font></td></tr> | ||
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| <tr><td bgcolor="#aa55cc"><tt> </tt></td><td> </td> | ||
| <td width="100%"><table width="100%" summary="list"><tr><td width="25%" valign=top><a href="mpyc.gf2x.html">mpyc.gf2x</a><br> | ||
| </td><td width="25%" valign=top></td><td width="25%" valign=top></td><td width="25%" valign=top></td></tr></table></td></tr></table><p> | ||
| <table width="100%" cellspacing=0 cellpadding=2 border=0 summary="section"> | ||
| <tr bgcolor="#ee77aa"> | ||
| <td colspan=3 valign=bottom> <br> | ||
| <font color="#ffffff" face="helvetica, arial"><big><strong>Classes</strong></big></font></td></tr> | ||
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| <tr><td bgcolor="#ee77aa"><tt> </tt></td><td> </td> | ||
| <td width="100%"><dl> | ||
| <dt><font face="helvetica, arial"><a href="builtins.html#object">builtins.object</a> | ||
| </font></dt><dd> | ||
| <dl> | ||
| <dt><font face="helvetica, arial"><a href="mpyc.bfield.html#BinaryFieldElement">BinaryFieldElement</a> | ||
| </font></dt></dl> | ||
| </dd> | ||
| </dl> | ||
| <p> | ||
| <table width="100%" cellspacing=0 cellpadding=2 border=0 summary="section"> | ||
| <tr bgcolor="#ffc8d8"> | ||
| <td colspan=3 valign=bottom> <br> | ||
| <font color="#000000" face="helvetica, arial"><a name="BinaryFieldElement">class <strong>BinaryFieldElement</strong></a>(<a href="builtins.html#object">builtins.object</a>)</font></td></tr> | ||
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| <tr bgcolor="#ffc8d8"><td rowspan=2><tt> </tt></td> | ||
| <td colspan=2><tt><a href="#BinaryFieldElement">BinaryFieldElement</a>(value)<br> | ||
| <br> | ||
| Common base class for binary field elements.<br> | ||
| <br> | ||
| Invariant: attribute 'value' is reduced.<br> </tt></td></tr> | ||
| <tr><td> </td> | ||
| <td width="100%">Methods defined here:<br> | ||
| <dl><dt><a name="BinaryFieldElement-__add__"><strong>__add__</strong></a>(self, other)</dt><dd><tt>Addition.</tt></dd></dl> | ||
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| <dl><dt><a name="BinaryFieldElement-__bool__"><strong>__bool__</strong></a>(self)</dt><dd><tt>Truth value testing.<br> | ||
| <br> | ||
| Return False if this field element is zero, True otherwise.<br> | ||
| Field elements can thus be used directly in Boolean formulas.</tt></dd></dl> | ||
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| <dl><dt><a name="BinaryFieldElement-__eq__"><strong>__eq__</strong></a>(self, other)</dt><dd><tt>Equality test.</tt></dd></dl> | ||
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| <dl><dt><a name="BinaryFieldElement-__iadd__"><strong>__iadd__</strong></a>(self, other)</dt><dd><tt>In-place addition.</tt></dd></dl> | ||
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| <dl><dt><a name="BinaryFieldElement-__ilshift__"><strong>__ilshift__</strong></a>(self, other)</dt><dd><tt>In-place left shift.</tt></dd></dl> | ||
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| <dl><dt><a name="BinaryFieldElement-__imul__"><strong>__imul__</strong></a>(self, other)</dt><dd><tt>In-place multiplication.</tt></dd></dl> | ||
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| <dl><dt><a name="BinaryFieldElement-__init__"><strong>__init__</strong></a>(self, value)</dt><dd><tt>Initialize self. See help(type(self)) for accurate signature.</tt></dd></dl> | ||
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| <dl><dt><a name="BinaryFieldElement-__int__"><strong>__int__</strong></a>(self)</dt><dd><tt>Extract polynomial field element as an integer.</tt></dd></dl> | ||
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| <dl><dt><a name="BinaryFieldElement-__irshift__"><strong>__irshift__</strong></a>(self, other)</dt><dd><tt>In-place right shift.</tt></dd></dl> | ||
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| <dl><dt><a name="BinaryFieldElement-__isub__"><strong>__isub__</strong></a> = <a href="#BinaryFieldElement-__iadd__">__iadd__</a>(self, other)</dt></dl> | ||
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| <dl><dt><a name="BinaryFieldElement-__itruediv__"><strong>__itruediv__</strong></a>(self, other)</dt><dd><tt>In-place division.</tt></dd></dl> | ||
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| <dl><dt><a name="BinaryFieldElement-__lshift__"><strong>__lshift__</strong></a>(self, other)</dt><dd><tt>Left shift.</tt></dd></dl> | ||
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| <dl><dt><a name="BinaryFieldElement-__mul__"><strong>__mul__</strong></a>(self, other)</dt><dd><tt>Multiplication.</tt></dd></dl> | ||
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| <dl><dt><a name="BinaryFieldElement-__neg__"><strong>__neg__</strong></a>(self)</dt><dd><tt>Negation.</tt></dd></dl> | ||
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| <dl><dt><a name="BinaryFieldElement-__pow__"><strong>__pow__</strong></a>(self, other)</dt><dd><tt>Exponentiation.</tt></dd></dl> | ||
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| <dl><dt><a name="BinaryFieldElement-__radd__"><strong>__radd__</strong></a> = <a href="#BinaryFieldElement-__add__">__add__</a>(self, other)</dt></dl> | ||
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| <dl><dt><a name="BinaryFieldElement-__repr__"><strong>__repr__</strong></a>(self)</dt><dd><tt>Return repr(self).</tt></dd></dl> | ||
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| <dl><dt><a name="BinaryFieldElement-__rlshift__"><strong>__rlshift__</strong></a>(self, other)</dt><dd><tt>Left shift (with reflected arguments).</tt></dd></dl> | ||
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| <dl><dt><a name="BinaryFieldElement-__rmul__"><strong>__rmul__</strong></a> = <a href="#BinaryFieldElement-__mul__">__mul__</a>(self, other)</dt></dl> | ||
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| <dl><dt><a name="BinaryFieldElement-__rrshift__"><strong>__rrshift__</strong></a>(self, other)</dt><dd><tt>Right shift (with reflected arguments).</tt></dd></dl> | ||
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| <dl><dt><a name="BinaryFieldElement-__rshift__"><strong>__rshift__</strong></a>(self, other)</dt><dd><tt>Right shift.</tt></dd></dl> | ||
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| <dl><dt><a name="BinaryFieldElement-__rsub__"><strong>__rsub__</strong></a> = <a href="#BinaryFieldElement-__add__">__add__</a>(self, other)</dt></dl> | ||
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| <dl><dt><a name="BinaryFieldElement-__rtruediv__"><strong>__rtruediv__</strong></a>(self, other)</dt><dd><tt>Division (with reflected arguments).</tt></dd></dl> | ||
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| <dl><dt><a name="BinaryFieldElement-__sub__"><strong>__sub__</strong></a> = <a href="#BinaryFieldElement-__add__">__add__</a>(self, other)</dt></dl> | ||
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| <dl><dt><a name="BinaryFieldElement-__truediv__"><strong>__truediv__</strong></a>(self, other)</dt><dd><tt>Division.</tt></dd></dl> | ||
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| <dl><dt><a name="BinaryFieldElement-reciprocal"><strong>reciprocal</strong></a>(self)</dt><dd><tt>Multiplicative inverse.</tt></dd></dl> | ||
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| <hr> | ||
| Class methods defined here:<br> | ||
| <dl><dt><a name="BinaryFieldElement-to_bytes"><strong>to_bytes</strong></a>(x)<font color="#909090"><font face="helvetica, arial"> from <a href="builtins.html#type">builtins.type</a></font></font></dt><dd><tt>Return an array of bytes representing the given list of polynomials x.</tt></dd></dl> | ||
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| <hr> | ||
| Static methods defined here:<br> | ||
| <dl><dt><a name="BinaryFieldElement-from_bytes"><strong>from_bytes</strong></a>(data)</dt><dd><tt>Return the list of integers represented by the given array of bytes.</tt></dd></dl> | ||
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| <hr> | ||
| Data descriptors defined here:<br> | ||
| <dl><dt><strong>value</strong></dt> | ||
| </dl> | ||
| <hr> | ||
| Data and other attributes defined here:<br> | ||
| <dl><dt><strong>__hash__</strong> = None</dl> | ||
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| <dl><dt><strong>ext_deg</strong> = None</dl> | ||
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| <dl><dt><strong>frac_length</strong> = 0</dl> | ||
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| <dl><dt><strong>modulus</strong> = None</dl> | ||
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| <dl><dt><strong>order</strong> = None</dl> | ||
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| </td></tr></table></td></tr></table><p> | ||
| <table width="100%" cellspacing=0 cellpadding=2 border=0 summary="section"> | ||
| <tr bgcolor="#eeaa77"> | ||
| <td colspan=3 valign=bottom> <br> | ||
| <font color="#ffffff" face="helvetica, arial"><big><strong>Functions</strong></big></font></td></tr> | ||
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| <tr><td bgcolor="#eeaa77"><tt> </tt></td><td> </td> | ||
| <td width="100%"><dl><dt><a name="-GF"><strong>GF</strong></a>(modulus)</dt><dd><tt>Create a Galois (finite) field for given irreducible polynomial.</tt></dd></dl> | ||
| <dl><dt><a name="-find_irreducible"><strong>find_irreducible</strong></a>(d)</dt><dd><tt>Find smallest irreducible polynomial of degree d satisfying given constraints.<br> | ||
| <br> | ||
| Constraints ... primitive, low weight w=3, 5</tt></dd></dl> | ||
| </td></tr></table> | ||
| </body></html> |
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