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Expression of type ExprTuple

from the theory of proveit.physics.quantum.QFT

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
from proveit.linear_algebra import Unitary
from proveit.logic import InSet
from proveit.numbers import Exp, NaturalPos, two
from proveit.physics.quantum.QFT import InverseFourierTransform
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda(n, Conditional(InSet(InverseFourierTransform(n), Unitary(Exp(two, n))), InSet(n, NaturalPos))))
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(n \mapsto \left\{{\mathrm {FT}}^{\dag}_{n} \in \textrm{U}\left(2^{n}\right) \textrm{ if } n \in \mathbb{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: 19
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 6
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 9
6Literal
7ExprTuple19, 10
8Operationoperator: 11
operand: 19
9Operationoperator: 13
operand: 15
10Literal
11Literal
12ExprTuple19
13Literal
14ExprTuple15
15Operationoperator: 16
operands: 17
16Literal
17ExprTuple18, 19
18Literal
19Variable