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Expression of type ExprTuple

from the theory of proveit.linear_algebra.tensors

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, ExprRange, ExprTuple, IndexedVar, Lambda, U, V, Variable, W, a, b, c, i, j, k
from proveit.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k
from proveit.linear_algebra import TensorProd
from proveit.logic import And, Equals, InSet
from proveit.numbers import one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda([a_1_to_i, b_1_to_j, c_1_to_k], Conditional(Equals(TensorProd(a_1_to_i, b_1_to_j, c_1_to_k), TensorProd(a_1_to_i, TensorProd(b_1_to_j), c_1_to_k)).with_wrapping_at(2), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), IndexedVar(U, sub_expr1)), one, i), ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), IndexedVar(V, sub_expr1)), one, j), ExprRange(sub_expr1, InSet(IndexedVar(c, sub_expr1), IndexedVar(W, sub_expr1)), one, k)))))
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left(\left(a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j}, c_{1}, c_{2}, \ldots, c_{k}\right) \mapsto \left\{\begin{array}{c} \begin{array}{l} \left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i}{\otimes} b_{1} {\otimes}  b_{2} {\otimes}  \ldots {\otimes}  b_{j}{\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) =  \\ \left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} \left(b_{1} {\otimes}  b_{2} {\otimes}  \ldots {\otimes}  b_{j}\right){\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) \end{array} \end{array} \textrm{ if } \left(a_{1} \in U_{1}\right) ,  \left(a_{2} \in U_{2}\right) ,  \ldots ,  \left(a_{i} \in U_{i}\right), \left(b_{1} \in V_{1}\right) ,  \left(b_{2} \in V_{2}\right) ,  \ldots ,  \left(b_{j} \in V_{j}\right), \left(c_{1} \in W_{1}\right) ,  \left(c_{2} \in W_{2}\right) ,  \ldots ,  \left(c_{k} \in W_{k}\right)\right..\right)
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameters: 14
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9, 10
7Literal
8ExprTuple11, 12, 13
9Operationoperator: 27
operands: 14
10Operationoperator: 27
operands: 15
11ExprRangelambda_map: 16
start_index: 42
end_index: 26
12ExprRangelambda_map: 17
start_index: 42
end_index: 43
13ExprRangelambda_map: 18
start_index: 42
end_index: 30
14ExprTuple19, 35, 21
15ExprTuple19, 20, 21
16Lambdaparameter: 52
body: 22
17Lambdaparameter: 52
body: 23
18Lambdaparameter: 52
body: 24
19ExprRangelambda_map: 25
start_index: 42
end_index: 26
20Operationoperator: 27
operands: 28
21ExprRangelambda_map: 29
start_index: 42
end_index: 30
22Operationoperator: 33
operands: 31
23Operationoperator: 33
operands: 32
24Operationoperator: 33
operands: 34
25Lambdaparameter: 52
body: 36
26Variable
27Literal
28ExprTuple35
29Lambdaparameter: 52
body: 39
30Variable
31ExprTuple36, 37
32ExprTuple49, 38
33Literal
34ExprTuple39, 40
35ExprRangelambda_map: 41
start_index: 42
end_index: 43
36IndexedVarvariable: 44
index: 52
37IndexedVarvariable: 45
index: 52
38IndexedVarvariable: 46
index: 52
39IndexedVarvariable: 47
index: 52
40IndexedVarvariable: 48
index: 52
41Lambdaparameter: 52
body: 49
42Literal
43Variable
44Variable
45Variable
46Variable
47Variable
48Variable
49IndexedVarvariable: 50
index: 52
50Variable
51ExprTuple52
52Variable