Determining the achromatic number is NP-hard ; determining if it is greater than a given number is NP-complete, as shown by Yannakakis and Gavril in 1978 by transformation from the minimum maximal matching problem.

Determining the QR decomposition of a symmetric tridiagonal matrix costs operations .< ref > James M. Ortega and Henry F. Kaiser, " The LL < sup > T </ sup > and QR methods for symmetric tridiagonal matrices ," The Computer Journal 6 ( 1 ), 99 – 101 ( 1963 ).</ ref >

Determining the satisfiability of a formula in conjunctive normal form where each clause is limited to at most three literals is NP-complete ; this problem is called " 3SAT ", " 3CNFSAT ", or " 3-satisfiability ".

Determining the substance ingested is often complicated by the body's natural processes ( see ADME ), as it is rare for a chemical to remain in its original form once in the body.

Determining the presence of both parts of this definition is not always straightforward, as hypoglycemic symptoms and effects are vague and can be produced by other conditions ; people with recurrently low glucose levels can lose their threshold symptoms so that severe neuroglycopenic impairment can occur without much warning, and many measurement methods ( especially glucose meters ) are imprecise at low levels.

Determining a precise value for a particular knot is difficult because many factors can affect a knot efficiency test: the type of fiber, the style of rope, the size of rope, whether it is wet or dry, how the knot is dressed before loading, how rapidly it is loaded, whether the knot is repeatedly loaded, and so on.

Determining which proteins are poly-ubiquitinated can be helpful in understanding how protein pathways are regulated.

Determining whether a given food should be classified as bread, cake, or pastry can be difficult.

Determining the penetrance of the C282Y allele can be influenced by when, in the course of a lifetime, homozygotes are evaluated by the medical community.

Determining the strength of different manufactures of pepper sprays can be confusing.

Determining whether an employee has custody or possession can be difficult.

Determining if and to what extent a person can transfer their learned knowledge can be a strong indication of the quality of the learning experience itself.

Determining whether a player is in " active play " can be complex.

Determining whether the victim obtained title or possession can present problems.

Determining the principal value of some of these functions can be obtained by decomposing the function into simpler ones whereby the principal value of the simple functions are straightforward to obtain.

Determining whether any changes have been made to a message ( or a file ), for example, can be accomplished by comparing message digests calculated before, and after, transmission ( or any other event ).

Determining the age and sex of birds in brown plumage can be very difficult.

Determining what records have enduring value can be challenging.

Determining the head of navigation can be subjective on many streams, as this point may vary greatly with the size of the ship being contemplated for navigation.

* Determining relative humidity: The percent relative humidity can be located at the intersection of the vertical dry bulb and diagonally down sloping wet bulb temperature lines.

Determining fraud committed by the health insurance companies can sometimes be found be comparing revenues from premiums paid against the expenditure by the health insurance companies on claims.

Determining forecast accuracy, like forecasting itself, can never be performed with certainty and so it is advisable to ensure that input data is measured and obtained as accurately as possible, the most appropriate forecasting methods are selected, and the forecasting process is conducted as rigorously as possible.

Determining whether a particular reaction is conrotatory or disrotatory can be accomplished by examining the molecular orbitals of each molecule.

Determining the optimal parameters in a model of this type is not trivial, and local numerical optimization methods such as gradient descent can be sensitive to initialization because of the presence of local minima of the training criterion.

Determining the authenticity of a prewar Gibson banjo can be a real challenge, for a variety of reasons:

* Leading / directing: Determining what needs to be done in a situation and getting people to do it.

Determining the distances to astronomical objects is crucial to understanding them, but the vast majority of objects are too far away for their distances to be directly determined.

Determining part of a protein's amino-acid sequence ( often one end ) by one of the above methods may be sufficient to enable the identification of a clone carrying the gene.

Determining such forces was required before building codes could specify the required strength of such buildings and such tests continue to be used for large or unusual buildings.

Now we consider the set of all normal sets, R. Determining whether R is normal or abnormal is impossible: If R were a normal set, it would be contained in the set of normal sets ( itself ), and therefore be abnormal ; and if R were abnormal, it would not be contained in the set of all normal sets ( itself ), and therefore be normal.

Determining latitude was relatively easy in that it could be found from the altitude of the sun at noon with the aid of a table giving the sun's declination for the day.

Determining an appropriate and safe exercise program is challenging and must be carefully individualized to each person being sure to account for all contraindications and precautions.

Determining which instructions would actually be encountered during a run of the program reduces to the proven-unsolvable halting problem.

Determining which clue is to be applied to which grid is part of the puzzle.

Determining whether a captive should be classified as a prisoner of war is the sole purpose of a competent tribunal.

Determining the appropriate discount rate is the key to properly valuing future cash flows, whether they be earnings or obligations.

Determining whether news is " good " or " bad " must be determined by the price action of the stock, because the market reaction may not match the tone of the news itself.

; Interpretation: Determining if an indication is of a type to be investigated.

Determining the poverty line is usually done by finding the total cost of all the essential resources that an average human adult consumes in one year.

" Determining the link between data breaches and identity theft is challenging, primarily because identity theft victims often do not know how their personal information was obtained ," and identity theft is not always detectable by the individual victims, according to a report done for the FTC.

Determining whether the navel is displaced is done by the following procedure,

Determining an absolute poverty line is usually done by finding the total cost of all the essential resources that an average human adult consumes in one year.