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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, pi, two
from proveit.physics.quantum.QPE import _m_domain, _phase, _two_pow_t
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [k]
sub_expr2 = Exp(e, Mult(two, pi, i, _phase, k))
sub_expr3 = Exp(e, Neg(frac(Mult(two, pi, i, k, m), _two_pow_t)))
expr = ExprTuple(Sum(index_or_indices = sub_expr1, summand = Mult(sub_expr2, sub_expr3), domain = _m_domain), Sum(index_or_indices = sub_expr1, summand = Mult(sub_expr3, sub_expr2), 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(\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), \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: 4
operand: 6
2Operationoperator: 4
operand: 7
3ExprTuple6
4Literal
5ExprTuple7
6Lambdaparameter: 50
body: 8
7Lambdaparameter: 50
body: 10
8Conditionalvalue: 11
condition: 13
9ExprTuple50
10Conditionalvalue: 12
condition: 13
11Operationoperator: 44
operands: 14
12Operationoperator: 44
operands: 15
13Operationoperator: 16
operands: 17
14ExprTuple19, 18
15ExprTuple18, 19
16Literal
17ExprTuple50, 20
18Operationoperator: 46
operands: 21
19Operationoperator: 46
operands: 22
20Operationoperator: 23
operands: 24
21ExprTuple26, 25
22ExprTuple26, 27
23Literal
24ExprTuple28, 29
25Operationoperator: 39
operand: 34
26Literal
27Operationoperator: 44
operands: 31
28Literal
29Operationoperator: 32
operands: 33
30ExprTuple34
31ExprTuple52, 48, 49, 35, 50
32Literal
33ExprTuple42, 36
34Operationoperator: 37
operands: 38
35Literal
36Operationoperator: 39
operand: 43
37Literal
38ExprTuple41, 42
39Literal
40ExprTuple43
41Operationoperator: 44
operands: 45
42Operationoperator: 46
operands: 47
43Literal
44Literal
45ExprTuple52, 48, 49, 50, 51
46Literal
47ExprTuple52, 53
48Literal
49Literal
50Variable
51Variable
52Literal
53Literal