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Expression of type ExprTuple

from the theory of proveit.linear_algebra.addition

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, ExprTuple, Lambda, N, k, vk
from proveit.linear_algebra import ScalarMult
from proveit.logic import InSet
from proveit.numbers import Exp, Interval, Mult, e, i, one, pi, two
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda(k, Conditional(ScalarMult(Exp(e, Mult(two, pi, i, k)), vk), InSet(k, Interval(one, N)))))
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(k \mapsto \left\{\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot k} \cdot v\left(k\right) \textrm{ if } k \in \{1~\ldotp \ldotp~N\}\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
1Lambdaparameter: 27
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9, 10
7Literal
8ExprTuple27, 11
9Operationoperator: 12
operands: 13
10Operationoperator: 14
operand: 27
11Operationoperator: 16
operands: 17
12Literal
13ExprTuple18, 19
14Variable
15ExprTuple27
16Literal
17ExprTuple20, 21
18Literal
19Operationoperator: 22
operands: 23
20Literal
21Variable
22Literal
23ExprTuple24, 25, 26, 27
24Literal
25Literal
26Literal
27Variable