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Expression of type ExprTuple

from the theory of proveit.numbers.multiplication

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, Variable, a, b, i, j
from proveit.core_expr_types import a_1_to_i, b_1_to_j
from proveit.logic import And, Equals, InSet
from proveit.numbers import Complex, Mult, one, zero
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], Conditional(Equals(Mult(a_1_to_i, zero, b_1_to_j), zero), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Complex), one, i), ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), Complex), one, j)))))
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}\right) \mapsto \left\{\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot 0\cdot b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j}\right) = 0 \textrm{ if } \left(a_{1} \in \mathbb{C}\right) ,  \left(a_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(a_{i} \in \mathbb{C}\right), \left(b_{1} \in \mathbb{C}\right) ,  \left(b_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(b_{j} \in \mathbb{C}\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: 2
body: 3
2ExprTuple17, 19
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operands: 7
5Operationoperator: 8
operands: 9
6Literal
7ExprTuple10, 18
8Literal
9ExprTuple11, 12
10Operationoperator: 13
operands: 14
11ExprRangelambda_map: 15
start_index: 25
end_index: 23
12ExprRangelambda_map: 16
start_index: 25
end_index: 26
13Literal
14ExprTuple17, 18, 19
15Lambdaparameter: 36
body: 20
16Lambdaparameter: 36
body: 21
17ExprRangelambda_map: 22
start_index: 25
end_index: 23
18Literal
19ExprRangelambda_map: 24
start_index: 25
end_index: 26
20Operationoperator: 28
operands: 27
21Operationoperator: 28
operands: 29
22Lambdaparameter: 36
body: 30
23Variable
24Lambdaparameter: 36
body: 31
25Literal
26Variable
27ExprTuple30, 32
28Literal
29ExprTuple31, 32
30IndexedVarvariable: 33
index: 36
31IndexedVarvariable: 34
index: 36
32Literal
33Variable
34Variable
35ExprTuple36
36Variable