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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 ExprTuple, k, m
from proveit.numbers import Exp, Mult, Neg, Sum, e, frac, i, one, 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(frac(one, _two_pow_t), Sum(index_or_indices = [k], summand = Mult(Exp(e, Neg(frac(Mult(two, pi, i, k, m), _two_pow_t))), Exp(e, Mult(two, pi, i, _phase, k))), domain = _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(\frac{1}{2^{t}}, \sum_{k = 0}^{2^{t} - 1} \left(\mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot m}{2^{t}}} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k}\right)\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
wrap_positionsposition(s) at which wrapping is to occur; 'n' is after the nth comma.()()('with_wrapping_at',)
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'leftleft('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1, 2
1Operationoperator: 33
operands: 3
2Operationoperator: 4
operand: 6
3ExprTuple39, 38
4Literal
5ExprTuple6
6Lambdaparameter: 46
body: 8
7ExprTuple46
8Conditionalvalue: 9
condition: 10
9Operationoperator: 40
operands: 11
10Operationoperator: 12
operands: 13
11ExprTuple14, 15
12Literal
13ExprTuple46, 16
14Operationoperator: 42
operands: 17
15Operationoperator: 42
operands: 18
16Operationoperator: 19
operands: 20
17ExprTuple22, 21
18ExprTuple22, 23
19Literal
20ExprTuple24, 25
21Operationoperator: 35
operand: 30
22Literal
23Operationoperator: 40
operands: 27
24Literal
25Operationoperator: 28
operands: 29
26ExprTuple30
27ExprTuple48, 44, 45, 31, 46
28Literal
29ExprTuple38, 32
30Operationoperator: 33
operands: 34
31Literal
32Operationoperator: 35
operand: 39
33Literal
34ExprTuple37, 38
35Literal
36ExprTuple39
37Operationoperator: 40
operands: 41
38Operationoperator: 42
operands: 43
39Literal
40Literal
41ExprTuple48, 44, 45, 46, 47
42Literal
43ExprTuple48, 49
44Literal
45Literal
46Variable
47Variable
48Literal
49Literal