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Expression of type ExprTuple

from the theory of proveit.physics.quantum.QPE

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, k, m
from proveit.logic import InSet
from proveit.numbers import Exp, Mult, Neg, e, frac, i, pi, two
from proveit.physics.quantum.QPE import _m_domain, _phase, _two_pow_t
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda(k, Conditional(Mult(Exp(e, Mult(two, pi, i, _phase, k)), Exp(e, Neg(frac(Mult(two, pi, i, k, m), _two_pow_t)))), InSet(k, _m_domain))))
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 \varphi \cdot k} \cdot \mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot m}{2^{t}}} \textrm{ if } k \in \{0~\ldotp \ldotp~2^{t} - 1\}\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: 41
body: 3
2ExprTuple41
3Conditionalvalue: 4
condition: 5
4Operationoperator: 35
operands: 6
5Operationoperator: 7
operands: 8
6ExprTuple9, 10
7Literal
8ExprTuple41, 11
9Operationoperator: 37
operands: 12
10Operationoperator: 37
operands: 13
11Operationoperator: 14
operands: 15
12ExprTuple17, 16
13ExprTuple17, 18
14Literal
15ExprTuple19, 20
16Operationoperator: 35
operands: 21
17Literal
18Operationoperator: 30
operand: 26
19Literal
20Operationoperator: 23
operands: 24
21ExprTuple43, 39, 40, 25, 41
22ExprTuple26
23Literal
24ExprTuple33, 27
25Literal
26Operationoperator: 28
operands: 29
27Operationoperator: 30
operand: 34
28Literal
29ExprTuple32, 33
30Literal
31ExprTuple34
32Operationoperator: 35
operands: 36
33Operationoperator: 37
operands: 38
34Literal
35Literal
36ExprTuple43, 39, 40, 41, 42
37Literal
38ExprTuple43, 44
39Literal
40Literal
41Variable
42Variable
43Literal
44Literal