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Ask Dan and Mike
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Ask Dan and Mike
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Macaulay2, version 1.7.0.1
with packages: ConwayPolynomials, Elimination, IntegralClosure, LLLBases,
PrimaryDecomposition, ReesAlgebra, TangentCone
i1 : x_(0,0) .. x_(2,4)
o1 = (x , x , x , x , x , x , x , x , x , x , x , x , x ,
0,0 0,1 0,2 0,3 0,4 1,0 1,1 1,2 1,3 1,4 2,0 2,1 2,2
----------------------------------------------------------------------------------
x , x )
2,3 2,4
o1 : Sequence
i2 : x_(0,0) .. z_(2,4)
o2 = (x , x , x , x , x , x , x , x , x , x , x , x , x ,
0,0 0,1 0,2 0,3 0,4 1,0 1,1 1,2 1,3 1,4 2,0 2,1 2,2
----------------------------------------------------------------------------------
x , x , y , y , y , y , y , y , y , y , y , y , y ,
2,3 2,4 0,0 0,1 0,2 0,3 0,4 1,0 1,1 1,2 1,3 1,4 2,0
----------------------------------------------------------------------------------
y , y , y , y , z , z , z , z , z , z , z , z , z ,
2,1 2,2 2,3 2,4 0,0 0,1 0,2 0,3 0,4 1,0 1,1 1,2 1,3
----------------------------------------------------------------------------------
z , z , z , z , z , z )
1,4 2,0 2,1 2,2 2,3 2,4
o2 : Sequence
i3 : foo = method ( Options => { Limit => 4 } )
o3 = foo
o3 : MethodFunctionWithOptions
i4 : viewHelp Options
i5 : path
o5 = {./, ../M2-Macaulay2/M2/Macaulay2/packages/,
----------------------------------------------------------------------------------
../M2-Macaulay2/M2/BUILD/dan/builds.tmp/mac64-master.production/Macaulay2/packages
----------------------------------------------------------------------------------
/, ../M2-Macaulay2/M2/BUILD/dan/builds.tmp/mac64-master.production/usr-dist/common
----------------------------------------------------------------------------------
/share/Macaulay2/}
o5 : List
i6 :
Process M2 finished
+ /Users/dan/src/M2/M2-Macaulay2/M2/BUILD/dan/builds.tmp/mac64-master.production/M2 --no-readline --print-width 177
Macaulay2, version 1.7.0.1
with packages: ConwayPolynomials, Elimination, IntegralClosure, LLLBases, PrimaryDecomposition, ReesAlgebra, TangentCone
-- loading ../../../Library/Application Support/Macaulay2/code/hom.m2
../../../Library/Application Support/Macaulay2/code/hom.m2:3:15:(3):[5]: error: assignment to protected global variable 'homomorphism'', originally defined at ../M2-Macaulay2/M2/Macaulay2/m2/modules2.m2:522:1:(1):
../../../Library/Application Support/Macaulay2/code/hom.m2:3:15:(3):[5]: --entering debugger (type help to see debugger commands)
../../../Library/Application Support/Macaulay2/code/hom.m2:3:15-3:17: --source code:
homomorphism' = method()
i1 :
../M2-Macaulay2/M2/Macaulay2/m2/setup.m2:111:27:(1):[5]: --entering debugger (type help to see debugger commands)
../M2-Macaulay2/M2/Macaulay2/m2/setup.m2:111:27-111:35: --source code:
ret = loadfun fullfilename;
i2 : exit
Process M2 finished
+ M2 --no-readline --print-width 177
Macaulay2, version 1.7
with packages: ConwayPolynomials, Elimination, IntegralClosure, LLLBases, PrimaryDecomposition, ReesAlgebra, TangentCone
-- loading ../../../Library/Application Support/Macaulay2/code/hom.m2
i1 : path
o1 = {./, ../../../Library/Application Support/Macaulay2/code/, ../../../Library/Application Support/Macaulay2/local/share/Macaulay2/, ../../../Library/Application
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Support/Macaulay2/local/common/share/Macaulay2/, /Applications/Macaulay2-1.7/share/Macaulay2/}
o1 : List
i2 : printWidth = 80
o2 = 80
i3 : path
o3 = {./, ../../../Library/Application Support/Macaulay2/code/,
---------------------------------------------------------------------------
../../../Library/Application Support/Macaulay2/local/share/Macaulay2/,
---------------------------------------------------------------------------
../../../Library/Application
---------------------------------------------------------------------------
Support/Macaulay2/local/common/share/Macaulay2/,
---------------------------------------------------------------------------
/Applications/Macaulay2-1.7/share/Macaulay2/}
o3 : List
i4 :
Process M2 finished
+ M2 --no-readline --print-width 177
Macaulay2, version 1.7
with packages: ConwayPolynomials, Elimination, IntegralClosure, LLLBases, PrimaryDecomposition, ReesAlgebra, TangentCone
i1 :
Process M2 finished
+ /Users/dan/src/M2/M2-Macaulay2/M2/BUILD/dan/builds.tmp/mac64-master.production/M2 --no-readline --print-width 177
Macaulay2, version 1.7.0.1
with packages: ConwayPolynomials, Elimination, IntegralClosure, LLLBases, PrimaryDecomposition, ReesAlgebra, TangentCone
i1 : printWidth = 80
o1 = 80
i2 : toString Elimination
o2 = Elimination
i3 : class oo
o3 = String
o3 : Type
i4 : Elimination
o4 = Elimination
o4 : Package
i5 : peek Elimination
o5 = Package{configuration file name => /Users/dan/Library/Application Support/Macaulay2/init-Elimination.m2 }
Dictionary => Elimination.Dictionary
documentation not loaded => true
example data files => MutableHashTable{}
example inputs => MutableHashTable{}
example results => MutableHashTable{}
exported mutable symbols => {}
exported symbols => {sylvesterMatrix, discriminant, resultant, eliminate}
index.html => /Users/dan/src/M2/M2-Macaulay2/M2/BUILD/dan/builds.tmp/mac64-master.production/usr-dist/common/share/doc/Macaulay2/Elimination/html/index.html
loadDepth => 1
Options => OptionTable{Authors => {{Name => Michael E. Stillman, Email => mike@math.cornell.edu}}}
AuxiliaryFiles => false
CacheExampleOutput => null
Certification => null
Configuration => OptionTable{}
Date => January 5, 2005
DebuggingMode => false
Headline => a package for elimination of variables
HomePage => null
InfoDirSection => Macaulay2 and its packages
PackageExports => {}
PackageImports => {}
Reload => false
Version => 1.0
package prefix => /Users/dan/src/M2/M2-Macaulay2/M2/BUILD/dan/builds.tmp/mac64-master.production/usr-dist/
private dictionary => Elimination#"private dictionary"
processed documentation => MutableHashTable{}
raw documentation => MutableHashTable{}
raw documentation database => /Users/dan/src/M2/M2-Macaulay2/M2/BUILD/dan/builds.tmp/mac64-master.production/usr-dist/x86_64-MacOS-10.10/lib/Macaulay2/x86_64-MacOS-10.10/Elimination/cache/rawdocumentation-dcba-8.db
source directory => /Users/dan/src/M2/M2-Macaulay2/M2/Macaulay2/packages/
source file => /Users/dan/src/M2/M2-Macaulay2/M2/Macaulay2/packages/Elimination.m2
test inputs => MutableHashTable{}
test number => 0
title => Elimination
undocumented keys => MutableHashTable{}
i6 : f = x -> x+3
o6 = f
o6 : FunctionClosure
i7 : f 444
o7 = 447
i8 : f "hi there"
stdio:6:11:(3):[1]: error: no method for binary operator + applied to objects:
-- "hi there" (of class String)
-- + 3 (of class ZZ)
i9 : g = method()
o9 = g
o9 : MethodFunction
i10 : g ZZ := x -> x+1234
o10 = {*Function[stdio:10:11-10:16]*}
o10 : FunctionClosure
i11 : g String := x -> x | "+1234"
o11 = {*Function[stdio:11:15-11:20]*}
o11 : FunctionClosure
i12 : g 3
o12 = 1237
i13 : g "3"
o13 = 3+1234
i14 : partition
o14 = partition
o14 : MethodFunction
i15 : help oo
o15 = partition -- partition a set or list by values of a function
************************************************************
Synopsis
========
* Usage:partition(f,L)
* Inputs:
* f, a function
* L, a visible list, or a tally
* Outputs:
* a hash table, whose keys are the possible values of the function f
on the elements of the list, set or tally L, and the corresponding
value of the hash table is the list, set or tally of elements of L
which take that value under f
Description
===========
+----------------------------------------+
|i1 : L = {1,3,6,5,3,1,2,8,8,8} |
| |
|o1 = {1, 3, 6, 5, 3, 1, 2, 8, 8, 8} |
| |
|o1 : List |
+----------------------------------------+
|i2 : partition(odd, L) |
| |
|o2 = HashTable{false => {6, 2, 8, 8, 8}}|
| true => {1, 3, 5, 3, 1} |
| |
|o2 : HashTable |
+----------------------------------------+
|i3 : partition(odd, set L) |
| |
|o3 = HashTable{false => set {2, 6, 8}} |
| true => set {1, 3, 5} |
| |
|o3 : HashTable |
+----------------------------------------+
|i4 : partition(odd, tally L) |
| |
|o4 = HashTable{false => Tally{2 => 1}} |
| 6 => 1 |
| 8 => 3 |
| true => Tally{1 => 2} |
| 3 => 2 |
| 5 => 1 |
| |
|o4 : HashTable |
+----------------------------------------+
The following example parititions the generators of an ideal by degree.
+-----------------------------------------------------------+
|i5 : R = QQ[a..f] |
| |
|o5 = R |
| |
|o5 : PolynomialRing |
+-----------------------------------------------------------+
|i6 : I = ideal"ab,ade,ac3,d4,b3,adf,f4,e10" |
| |
| 3 4 3 4 10 |
|o6 = ideal (a*b, a*d*e, a*c , d , b , a*d*f, f , e ) |
| |
|o6 : Ideal of R |
+-----------------------------------------------------------+
|i7 : partition(f -> first degree f, flatten entries gens I)|
| |
|o7 = HashTable{2 => {a*b} } |
| 3 |
| 3 => {a*d*e, b , a*d*f} |
| 3 4 4 |
| 4 => {a*c , d , f } |
| 10 |
| 10 => {e } |
| |
|o7 : HashTable |
+-----------------------------------------------------------+
See also
========
* "tally" -- tally the elements of a list or sequence
* "partitions" -- list the partitions of an integer
Ways to use partition :
=======================
* partition(Function,Tally)
* partition(Function,VisibleList)
o15 : DIV
i16 : partition ( x -> abs x , {3,-3,4,-4,-6,-7} )
o16 = HashTable{3 => {3, -3}}
4 => {4, -4}
6 => {-6}
7 => {-7}
o16 : HashTable
i18 : o16#4
o18 = {4, -4}
o18 : List
i19 : partition ( x -> even x , {3,-3,4,-4,-6,-7} )
o19 = HashTable{false => {3, -3, -7}}
true => {4, -4, -6}
o19 : HashTable
i20 : QQ[x]===QQ[x]
o20 = false
i21 : x
o21 = x
o21 : QQ[x]
i22 : R = QQ[x]
o22 = R
o22 : PolynomialRing
i23 : ring x
o23 = R
o23 : PolynomialRing
i24 : ring x === R
o24 = true
i25 : ring x == R
stdio:25:8:(3): error: no method for binary operator == applied to objects:
-- R (of class PolynomialRing)
-- == R (of class PolynomialRing)
i26 : instance(x,R)
o26 = true
i27 : 4.5
o27 = 4.5
o27 : RR (of precision 53)
i28 : ring oo
o28 = RR
53
o28 : RealField
i29 : class 4.5
o29 = RR
o29 : InexactFieldFamily
i30 : instance(4.5, ring 4.5)
o30 = false
i31 : fold(times,{1,2,3,4})
o31 = 24
i32 : times {1,2,3,4}
o32 = {1, 2, 3, 4}
o32 : List
i33 : times (1,2,3,4)
o33 = 24
i34 : product {1,2,3,4}
o34 = 24
i35 : R = QQ[a_1 .. a_10]
o35 = R
o35 : PolynomialRing
i36 : I = ideal(a_1, a_2, a_3+a_4, a_9^6)
6
o36 = ideal (a , a , a + a , a )
1 2 3 4 9
o36 : Ideal of R
i37 : support I
o37 = {a , a , a , a , a }
1 2 3 4 9
o37 : List
i38 : S = QQ[support I]
o38 = S
o38 : PolynomialRing
i39 : sub(I,S)
6
o39 = ideal (a , a , a + a , a )
1 2 3 4 9
o39 : Ideal of S
i40 : vars R
o40 = | a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 |
1 10
o40 : Matrix R <--- R
i41 : vars S
o41 = | a_1 a_2 a_3 a_4 a_9 |
1 5
o41 : Matrix S <--- S
i42 : hilbertSeries S^1
1
o42 = --------
5
(1 - T)
o42 : Expression of class Divide
i43 : h = oo
1
o43 = --------
5
(1 - T)
o43 : Expression of class Divide
i44 : numerator h
o44 = 1
o44 : ZZ[T]
i45 : T
o45 = T
o45 : Symbol
i46 : numerator h + T
stdio:46:13:(3): error: no method for binary operator + applied to objects:
-- 1 (of class ZZ[T])
-- + T (of class Symbol)
i48 : use ring numerator h
o48 = ZZ[T]
o48 : PolynomialRing
i49 : T
o49 = T
o49 : ZZ[T]
i50 : numerator h + T
o50 = 1 + T
o50 : ZZ[T]
i51 : denominator h
5
o51 = (1 - T)
o51 : Expression of class Product
i52 : peek oo
5
o52 = Product{(1 - T) }
i53 : value denominator h
2 3 4 5
o53 = 1 - 5T + 10T - 10T + 5T - T
o53 : ZZ[T]
i54 : value h
stdio:54:1:(3): error: not implemented : fraction fields of rings with inverses
i55 : dictionaryPath
o55 = {Macaulay2Doc.Dictionary, SimpleDoc.Dictionary, User#"private dictionary",
--------------------------------------------------------------------------
User.Dictionary, Elimination.Dictionary, LLLBases.Dictionary,
--------------------------------------------------------------------------
IntegralClosure.Dictionary, PrimaryDecomposition.Dictionary,
--------------------------------------------------------------------------
Classic.Dictionary, TangentCone.Dictionary, ReesAlgebra.Dictionary,
--------------------------------------------------------------------------
ConwayPolynomials.Dictionary, Core.Dictionary, OutputDictionary,
--------------------------------------------------------------------------
PackageDictionary}
o55 : List
i56 : f = x -> (
g := t -> t+3;
g x + g x)
o56 = f
o56 : FunctionClosure
i57 : f 5
o57 = 16
i58 : g
o58 = g
o58 : MethodFunction
i59 : f = x -> t -> x+t
o59 = f
o59 : FunctionClosure
i60 : (f 4) 5
o60 = 9
i61 :
-----------------------------------------------------------------------------
einsteinium$ pwd
/Users/dan/src/M2/M2-Macaulay2/M2/Macaulay2/packages
einsteinium$ git status
On branch Hom-functoriality
Your branch is up-to-date with 'dan/Hom-functoriality'.
Changes not staged for commit:
(use "git add <file>..." to update what will be committed)
(use "git checkout -- <file>..." to discard changes in working directory)
modified: ../m2/modules2.m2
Untracked files:
(use "git add <file>..." to include in what will be committed)
DanPackage.m2
../../compose.m2
no changes added to commit (use "git add" and/or "git commit -a")
einsteinium$ git stash save
Saved working directory and index state WIP on Hom-functoriality: fb07cb8 new strategy for compose(Module,Module,Module)
HEAD is now at fb07cb8 new strategy for compose(Module,Module,Module)
einsteinium$ git checkout -b demonstrate-pull-request
Switched to a new branch 'demonstrate-pull-request'
einsteinium$ git status
On branch demonstrate-pull-request
Untracked files:
(use "git add <file>..." to include in what will be committed)
DanPackage.m2
../../compose.m2
nothing added to commit but untracked files present (use "git add" to track)
einsteinium$ git add DanPackage.m2
einsteinium$ git status
On branch demonstrate-pull-request
Changes to be committed:
(use "git reset HEAD <file>..." to unstage)
new file: DanPackage.m2
Changes not staged for commit:
(use "git add <file>..." to update what will be committed)
(use "git checkout -- <file>..." to discard changes in working directory)
modified: =distributed-packages
Untracked files:
(use "git add <file>..." to include in what will be committed)
../../compose.m2
einsteinium$ git diff
diff --git a/M2/Macaulay2/packages/=distributed-packages b/M2/Macaulay2/packages/=distributed-packages
index ef97032..4ac19d2 100644
--- a/M2/Macaulay2/packages/=distributed-packages
+++ b/M2/Macaulay2/packages/=distributed-packages
@@ -113,3 +113,4 @@ TateOnProducts
LatticePolytopes
FiniteFittingIdeals
HigherCIOperators
+DanPackage
einsteinium$ git add =distributed-packages
einsteinium$ git status
On branch demonstrate-pull-request
Changes to be committed:
(use "git reset HEAD <file>..." to unstage)
modified: =distributed-packages
new file: DanPackage.m2
Untracked files:
(use "git add <file>..." to include in what will be committed)
../../compose.m2
einsteinium$ git commit
Waiting for Emacs...
[demonstrate-pull-request ba139e3] my new package
2 files changed, 2 insertions(+)
create mode 100644 M2/Macaulay2/packages/DanPackage.m2
einsteinium$ git log -1
commit ba139e3d2d0ab37789f173478e2adbe0b070de70
Author: Daniel R. Grayson <dan@math.uiuc.edu>
Date: Fri May 29 09:29:27 2015 -0600
my new package
... which is wonderful
einsteinium$
einsteinium$ git status
On branch demonstrate-pull-request
Untracked files:
(use "git add <file>..." to include in what will be committed)
../../compose.m2
nothing added to commit but untracked files present (use "git add" to track)
einsteinium$ git remote -v
dan git@github.com:DanGrayson/M2 (fetch)
dan git@github.com:DanGrayson/M2 (push)
dan-ssh http://github.com/DanGrayson/M2 (push)
dan-ssh http://github.com/DanGrayson/M2 (fetch)
david git@github.com:eisenbud/M2 (push)
david git@github.com:eisenbud/M2 (fetch)
mike git@github.com:MikeStillman/M2 (fetch)
mike git@github.com:MikeStillman/M2 (push)
origin git@github.com:Macaulay2/M2 (push)
origin git@github.com:Macaulay2/M2 (fetch)
origin-ssh http://github.com/Macaulay2/M2 (fetch)
origin-ssh http://github.com/Macaulay2/M2 (push)
einsteinium$ git push dan-ssh demonstrate-pull-request
Username for 'https://github.com': DanGrayson
Password for 'https://DanGrayson@github.com':
Counting objects: 7, done.
Delta compression using up to 8 threads.
Compressing objects: 16% (1/6)
Compressing objects: 33% (2/6)
Compressing objects: 50% (3/6)
Compressing objects: 66% (4/6)
Compressing objects: 83% (5/6)
Compressing objects: 100% (6/6)
Compressing objects: 100% (6/6), done.
Writing objects: 14% (1/7)
Writing objects: 28% (2/7)
Writing objects: 42% (3/7)
Writing objects: 57% (4/7)
Writing objects: 71% (5/7)
Writing objects: 85% (6/7)
Writing objects: 100% (7/7)
Writing objects: 100% (7/7), 580 bytes | 0 bytes/s, done.
Total 7 (delta 5), reused 0 (delta 0)
To http://github.com/DanGrayson/M2
* [new branch] demonstrate-pull-request -> demonstrate-pull-request
einsteinium$ git fetch dan-ssh