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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
from proveit.numbers import Abs, Exp, Mod, Mult, Round, four, frac, pi, two
from proveit.physics.quantum.QPE import SubIndexed, _alpha, _phase, _two_pow_t
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(frac(four, Exp(pi, two)), Exp(Abs(SubIndexed(_alpha, [Mod(Round(Mult(_two_pow_t, _phase)), _two_pow_t)])), two))
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{4}{\pi^{2}}, \left|\alpha_{round\left(2^{t} \cdot \varphi\right) ~\textup{mod}~ 2^{t}}\right|^{2}\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: 3
operands: 4
2Operationoperator: 27
operands: 5
3Literal
4ExprTuple6, 7
5ExprTuple8, 29
6Literal
7Operationoperator: 27
operands: 9
8Operationoperator: 10
operand: 13
9ExprTuple12, 29
10Literal
11ExprTuple13
12Literal
13Operationoperator: 14
operand: 16
14Literal
15ExprTuple16
16Operationoperator: 17
operands: 18
17Literal
18ExprTuple19, 25
19Operationoperator: 20
operand: 22
20Literal
21ExprTuple22
22Operationoperator: 23
operands: 24
23Literal
24ExprTuple25, 26
25Operationoperator: 27
operands: 28
26Literal
27Literal
28ExprTuple29, 30
29Literal
30Literal