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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, _t, _two_pow_t
In [2]:
# build up the expression from sub-expressions
sub_expr1 = frac(one, Exp(two, frac(_t, two)))
sub_expr2 = Sum(index_or_indices = [k], summand = Mult(Exp(e, Mult(two, pi, i, _phase, k)), Exp(e, Neg(frac(Mult(two, pi, i, k, m), _two_pow_t)))), domain = _m_domain)
expr = ExprTuple(Mult(sub_expr1, Mult(sub_expr1, sub_expr2)), Mult(Exp(sub_expr1, two), sub_expr2))
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^{\frac{t}{2}}} \cdot \left(\frac{1}{2^{\frac{t}{2}}} \cdot \left(\sum_{k = 0}^{2^{t} - 1} \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}}}\right)\right)\right), \left(\frac{1}{2^{\frac{t}{2}}}\right)^{2} \cdot \left(\sum_{k = 0}^{2^{t} - 1} \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}}}\right)\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: 52
operands: 3
2Operationoperator: 52
operands: 4
3ExprTuple10, 5
4ExprTuple6, 9
5Operationoperator: 52
operands: 7
6Operationoperator: 54
operands: 8
7ExprTuple10, 9
8ExprTuple10, 60
9Operationoperator: 11
operand: 14
10Operationoperator: 45
operands: 13
11Literal
12ExprTuple14
13ExprTuple51, 15
14Lambdaparameter: 58
body: 17
15Operationoperator: 54
operands: 18
16ExprTuple58
17Conditionalvalue: 19
condition: 20
18ExprTuple60, 21
19Operationoperator: 52
operands: 22
20Operationoperator: 23
operands: 24
21Operationoperator: 45
operands: 25
22ExprTuple26, 27
23Literal
24ExprTuple58, 28
25ExprTuple61, 60
26Operationoperator: 54
operands: 29
27Operationoperator: 54
operands: 30
28Operationoperator: 31
operands: 32
29ExprTuple34, 33
30ExprTuple34, 35
31Literal
32ExprTuple36, 37
33Operationoperator: 52
operands: 38
34Literal
35Operationoperator: 47
operand: 43
36Literal
37Operationoperator: 40
operands: 41
38ExprTuple60, 56, 57, 42, 58
39ExprTuple43
40Literal
41ExprTuple50, 44
42Literal
43Operationoperator: 45
operands: 46
44Operationoperator: 47
operand: 51
45Literal
46ExprTuple49, 50
47Literal
48ExprTuple51
49Operationoperator: 52
operands: 53
50Operationoperator: 54
operands: 55
51Literal
52Literal
53ExprTuple60, 56, 57, 58, 59
54Literal
55ExprTuple60, 61
56Literal
57Literal
58Variable
59Variable
60Literal
61Literal